cos 15 - sin 15 = 1/2


prove that :​

Answers

Answer 1

Answer:

Cos(15) = Cos(45-30)

Sin(15) = Sin(45-30)

Cos(45-30) - Sin(45-30)

Simplifying both brackets

Recall

Cos(A+B) = CosACosB - SinASinB (For cosine... The sign is always the opposite during expansion. If you look... Cos(A+B) became negative during its expansion;So if It was Cos(A–B)... Its expansion is CosACosB + SinASinB)]

Sin(A+B) = SinACosB + CosASinB

Now let's go!

Cos(45-30) = Cos45Cos30 + Sin45Sin30

From Trig

Cos45 = 1/√2

Cos30 = √3/2

Sin45 = 1/√2

Sin30 = 1/2

Substituting

Cos(45-30) = (1/√2).(√3/2) + (1/√2).(1/2)

= √3/(2√2) + 1/(2√2)

= 1 + √3/(2√2).

For

Sin(45 - 30)

= Sin45cos30 – Cos45Sin30

= (1/√2).(√3/2) – (1/√2).(1/2)

= √3/(2√2) – 1/2√2

= √3 – 1/(2√2)

So the question was

Cos15 - Sin15

Substituting...

1 + √3 / 2√2 – (√3 - 1)/ 2√2

When the Minus interacts with the parenthesis

We have

1 + √3 - √3 + 1 / (2√2)

= 2/2√2

= 1/√2.

THE ANSWER IS 1/2 AND NOT 1/2.

YOU CAN VERIFY THIS WITH YOUR CALCULATOR ALSO.

YOU'LL HAVE 0.7071 WHICH IS SAME AS 1/2.

HAVE A GREAT DAY!


Related Questions

Help urgent please be certain

Answers

Answer:

17 =x

Step-by-step explanation:

The angles are vertical angles, so they are equal

51 = 3x

Divide each side by 3

51/3 = 3x/3

17 =x

Answer:

C) 17

Step-by-step explanation:

Since the angle needed to be 51˚ we need to figure out which number that multiplies by 3 will get to 51˚ so 17 is the answer

17 times 3 is 51˚

Ian bought a used car. The value, y , of the car x years after his purchase is modeled by the equation y = 6500(0.875)x . What was the value of the car when Ian bought it?

Answers

Answer:

6500

Step-by-step explanation:

y = 6500(0.875)^x

When bought x = 0

y = 6500(0.875)^0

A number raise to 0 equals 1

y = 6500 * 1

y = 6500

make p the subject of the relation A is equal to 1/2 ( p + b) h​

Answers

Answer:

2A /h  -b =p

If you need it with a common denominator

(2A -bh)/h = p

Step-by-step explanation:

A = 1/2 ( p+b)h

Multiply each side by 2

2A =  ( p+b)h

Divide by h

2A/h =  ( p+b)h/h

2A/h =  ( p+b)

Subtract b

2A/h   -b =   p+b -b

2A /h  -b =p

If you need it with a common denominator

(2A -bh)/h = p

20.
Determine the type and number of solutions of 7x2 + 3x + 8 = 0.
two imaginary solutions
two real solutions
one real solution and one imaginary solution
one real solution

Answers

two real solutions

b2-4ac>0

one real solutions and one imaginary solution

b2-4ac=0

no real solution

b2-4ac<0

a=7

b=3

c=8

(3)^2-4(7)(8)=-215 no real solution

A wooden board has a volume of 0.225 cubic m and a mass of 146.25 kilograms.
What is the density of the board?

Answers

Answer:

650 kg/m³

Step-by-step explanation:

The density is the ratio of mass to volume. The volume is the product of the dimensions of the prism.

 density = (146.25 kg)/((1.5 m)(0.75 m)(0.2 m)) = 146.25/0.225 kg/m³

 = 650 kg/m³

Hope this answer helps you :)

Have a great day

Mark brainliest

Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jennifer to complete this job on her ow

Answers

Answer:

If they would both work at the same speed they would each take 4 hours to complete the room. So in total they would work 8 hours. But because Carl can finish three hours before Jennifer 3 hours of the eight already got to Jennifer. Then we divide the resting 5 hours by the two and then we have:

Jennifer:

3+2,5=5,5

Carl:

2,5

( if I am right)

5 + 3 + 7 = 5 + 7 + 3
O A. True
B. False

Answers

Answer:

True

Step-by-step explanation:

5+3+7=5+7+3

15=15

Hence proved.

Find the vertex of y=-2(x-4)2 + 3 and identify it as a minimum or a maximum

Answers

Answer:

Step-by-step explanation:

Remark

The minus sign in front of the 2 means that the quadratic has a maximum.

The vertex is already written in vertex form.

y= - 2 (x - 4)^2 + 3

The vertex is (4,3). Notice that the sign on the 4 changes. What you are trying to do is find the maximum point. That occurs when the minus number is made to be 0, which occurs when x = 4. The maximum y value is 3 when that happens.

I have enclosed a graph to show you all the details. Notice the maximum is when I've said it was and the roots have also been calculated.

HELP! HELP!PLEASSSSSEEEEEEEEEE HEEEEEEEELLLLLLPPPP!

Answers

Answer = 20%

Explanation:

% of TV = 65%
% of Newspaper = 40%
% of TV + Newspaper = 25%

% of TV but not Newspaper = 65% - 25% = 40%
% of Newspaper but not TV = 40% - 25% = 15%

% of TV only + Newspaper only + TV and Newspaper = 40% + 15% + 25% = 80%

% of neither TV nor Newspaper = 100% - 80% = 20%

Help please I don't really understand what to do here, so if somebody could find the answer that'd be great!

Answers

Answer:

See below.

Step-by-step explanation:

4.2 is 4 and 2 tenths.

4 is 40 tenths.

That means that 4.2 is 40 tenths plus 2 tenths, or 42 tenths.

First line: 4.2 / 6 = 42 tenths / 6

In the second line, we divide 42 tenths by 6. Since 42 divided by 6 = 7, then 42 tenths divided by 6 equals 7 tenths.

Second line: 4.2 / 6 = 7 tenths

In the third line, we write 7 tenths as a number. 7 tenths is the same as 0.7.

Third line: 4.2 / 6 = 0.7

what is a way of representing how the members of one group are related to the members of another group

Answers

Answer: Face

Step-by-step explanation: look at there face?

Otsottex pudoyxyoc oydxyldlydyl dyodyoxkyd yssodyslud Todd today’s yodtdyoup it’s dot dots yddyodoydyo Godoy dots yldyodoyd dydodyyoyo

help,very easy question but i can't understand

Answers

Answer:

10

Step-by-step explanation:

10 is the greatest common factor that you can divide into both 40 and 50.

Answer:

10

Step-by-step explanation:

Try and find the prime factorization of 40 and 50.

40=2*2*2*5

50=2*5*5

Multiply the prime  factors that are common to both numbers.

2*5=10

PLZ HELP ILL GIVE BRAINLIST

Answers

Answer:

[tex]14 \: 26 \: 6.5[/tex]

14

26

6.5

Which is a simplified form of the expression -3p – 4 + 4p + 8?
A. -p - 4
B. 2p - 4
C. p + 4
D. 7p + 4

Answers

Answer:

C

Step-by-step explanation:

-3p – 4 + 4p + 8

Simplify by combining like terms

-3p + 4p = p

-4 + 8 = 4

The expression in it's simplest form would be p + 4

Answer:

The answer is C.

Step-by-step explanation:

-3p - 4 + 4p + 8 can be grouped into:

-3p + 4p - 4 + 8.

If you add the p's together and the numbers together, your answer should be:

p + 4.

PLS HELPPPPP<3tyyyyyy this is due today! so please helppp tysmmm and have a great night or morning! :) (spam)

Answers

Answer:

#3: 4

#7: >

#8: =

#9: >

#10: <

Step-by-step explanation:

1 decimeter = 10 centimeters

1 meter = 10 decimeters

1 kilometer = 1,000 meters

(12y²+17y-4)+(9y²-13y+3)​

Answers

(12y^2 + 17y - 4) + (9y^2 - 13y + 3)

= 12y^2 + 17y - 4 + 9y^2 - 13y + 3

= 21y^2 + 4y - 1

Pre-calc, image attached

Answers

Answer:

[tex]\lim_{x \to 7} \frac{\sqrt{x+2}-3 }{x-7} = \frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\lim_{x \to 7} \frac{\sqrt{x+2}-3 }{x-7}[/tex]

[tex]\frac{\sqrt{x+2}-3 }{x-7}[/tex]

[tex]\frac{\frac{1}{2} (x+2)^{-\frac{1}{2} }}{1}[/tex] <-- Take derivative of numerator and denominator expressions

[tex]{\frac{1}{2} (x+2)^{-\frac{1}{2} }}[/tex] <-- Simplify

[tex]\frac{1}{2}(\frac{1}{\sqrt{x+2} })[/tex] <-- Rewrite

[tex]\frac{1}{2}(\frac{1}{\sqrt{7+2} })[/tex] <-- Use direct substitution and plug in the limit x=7

[tex]\frac{1}{2}(\frac{1}{\sqrt{9} })[/tex]

[tex]\frac{1}{2}(\frac{1}3 })[/tex]

[tex]\frac{1}{6}[/tex]

Therefore, [tex]\lim_{x \to 7} \frac{\sqrt{x+2}-3 }{x-7} = \frac{1}{6}[/tex]

In the diagram, BC = 10 and AD = 14. Find MN.
A
2.
B)
12
C)
14
D)
24

Answers

Answer:

I think D 24 but i am not sure

Answer:

B)12

Step-by-step explanation:

I took the test

What is the perimeter of triangle XYZ?

Answers

Answer:

126

Step-by-step explanation:

The dimensions of a rectangular prism are shown in the table.
Length: 10 in
Width: 12 in
Height: 16 in
What is the surface area of the rectangular prism?

Answers

Answer: 944 in^2.



Explanation: The formula for the surface area of a rectangular prism is 2(WL+HL+HW) where W=width, L=length, and H=height. Since all the dimensions are given, you simply need to substitute each value into the formula. Thus, the formula becomes: 2(12*10+16*10+16*12)
=2(120+160+192)
=2*472
=944 (solve using the order of operations)




Hope this helps シ
994 in^2 an the formula is S=2LH+2LW+2WH

If f (x) = -2x2 + 6, find f (-3).

Answers

Answer:

Step-by-step explanation:

Answer:

f(- 3) = - 12

Step-by-step explanation:

To find f(- 3) substitute x = - 3 into f(x) , that is

f(- 3) = -2(- 3)² + 6 = -2(9) + 6 = - 18 + 6 = - 12

14. A computer originally costs $1550 is on sale for 15% off. How much is
the discount? *

A. $232.50
B. $23.25
C. $15.00
D. $1,317.50

Dont mind the blue. I hit B by accident.

Answers

232.50

1550 / 100 is 15.5 so 15.5 = 1%, 15.5 x 15 = 232.5 = 15%

Select the true statement about Triangle ABC.

Answers

Answer:b

Step-by-step explanation:

Help please hurry NO LINKS!!!
Special Right Triangles (Radical Answers)

Answers

Answer:

[tex]2\sqrt{6}[/tex] = x

Step-by-step explanation:

We can use the Tan ratio to figure this out;

[tex]Tan(60) = \frac{x}{\sqrt{8} }[/tex]

Tan(60) * [tex]\sqrt{8}[/tex] = x

[tex]2\sqrt{6}[/tex] = x

Hope this helps!

The polygons are similar. The area of one polygon is given. Find the area of the other polygon.

3 cm
12 cm
A-96 cm?

Answers

Answer:

Hello! answer: area is 6 cm2

Step-by-step explanation:

Triangle area formula: base × height ÷ 2 or base × height × 1/2 so...

12 × 16 = 192 192 ÷ 2 = 96

12 ÷ 4 = 3

16 ÷ 4 = 4

3 × 4 = 12 12 ÷ 2 = 6 therefore the area is 6 hope that helps!

Answer:

6 cm²

Step-by-step explanation:

Given the sides of 2 similar figures in the ratio a : b , then

ratio of areas = a² : b²

Here the ratio of sides = 3 : 12 = 1 : 4

ratio of areas = 1² : 4² = 1 : 16

That is the area of the larger polygon is 16 times the smaller, so

area of smaller polygon = 96 ÷ 16 = 6 cm²

hey do y’all know how to solve this?:(

Answers

Answer:

27 m

Step-by-step explanation:

We know that ABC = 42 degrees

and side length BC = 24m

tan42 = 24m/a

a = 24/tan42

a = 26.65m

round to nearest whole number

= 27 m

Answer:

12 or 16 m

Step-by-step explanation:

I NEED HELP PLEASE !!

Answers

Answer:14=x

Step-by-step explanation:

Question: What is the probability of rolling one or more tails?
P(T > 1) = P(T = 1) + P(T = 2) = \ + 1
(Enter as a reduced fraction using / for the fraction bar.)

Answers

Odk I just don’t know sorry

Belleview High School has 12 chaperones for 198 students on a field trip. Which of the following schools has the same ratio of chaperones to students?

Answers

Answer:

The ratio for this school is 12/186 which gives us 2/31. Just check which option has the same ratio and that will be your answer.

Step-by-step explanation:

Answer:

There is no other schools listed so I cant answer the question

Step-by-step explanation:

Which statement is not true about the absolute value of -6?
A. It descrlbes the distance between -6 and 0 on the number line.
B. It equals the absolute value of 6.
C. It describes the distance between 6 and -6 on the number line.
D. It can be expressed as |-6|.

Answers

Answer:

C

Step-by-step explanation:

All the other answers are the same worded differently except c.

The distance between 6 and -6 is 12 so that is not correct for the absolute value of -6

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