prove the above question and i will give you....​

Prove The Above Question And I Will Give You....

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the identity

cos²A - sin²B = cos(A + B) . cos(A - B)

Here A = [tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] , B = [tex]\frac{\pi }{8}[/tex] - [tex]\frac{A}{2}[/tex]

Consider the left side

cos²([tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] ) - sin²( [tex]\frac{\pi }{8}[/tex] - [tex]\frac{A}{2}[/tex] )

= cos([tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] + [tex]\frac{\pi }{8}[/tex] - [tex]\frac{A}{2}[/tex] ) × cos([tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] - [tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] )

= cos ([tex]\frac{\pi }{4}[/tex] ) × cos ( A)

= [tex]\frac{1}{\sqrt{2} }[/tex] cosA

=  right side , thus proven


Related Questions

Mrs. Logan traveled at an average speed of 55 miles per hour for 3.5 hours and then traveled at an average speed of 60 miles per hour for 2.5 hours. What was the total distance in miles that Ms. Logan traveled during this time?

Answers

Answer:

55 mph for 3.5 hours would be 192.5 miles. 60 mph for 2.5 hours would be 150 miles. The total of mile Ms. Logan went is 342.5.

PLZ HELP!!!

What is 9 + 10?

Answers

The answer is 19 lol

Answer:

21.

Step-by-step explanation:

M a t h .

From the top of a light house 60 meters high with its base at sea level, the angle of depression to a boat is 15o. What is the distance of the boat from the foot of the light house?

Answers

Answer:

Distance between boat and light house = 223.88 meter (Approx.)

Step-by-step explanation:

Given:

Height of light house = 60 meters

Angle of depression to boat = 15°

Find:

Distance between boat and light house

Computation:

Using trigonometry application:

Tanθ = Perpendicular / Base

Tan 15 = Height of light house / Distance between boat and light house

0.268 = 60 / Distance between boat and light house

Distance between boat and light house = 60 / 0.268

Distance between boat and light house = 223.88 meter (Approx.)

Factor 24m – 12p + 72 to identify the equivalent expressions.

Answers

Answer:

C. 12 (2m - p + 6)

Step-by-step explanation:

just distribute

12 (2m) = 12m

12 (- p) = -12p

12 (6) = 72

Please help me please I really need help

Answers

Answer:

See below

Step-by-step explanation:

The answer is attached

g(x)=x-3
f(x) = -2x + 2
Find g(f(x)

Answers

Answer:

- 2x - 1

Step-by-step explanation:

[tex]g(x)=x-3 \\ f(x) = -2x + 2 \\ g(f(x)) = ( - 2x + 2) - 3 \\ g(f(x)) = - 2x + 2 - 3 \\ g(f(x)) = - 2x - 1[/tex]

If the sum of the measures of the interior angles of a polygon is 1980 degrees, how many sides does it have? I need an explanation to this!

Answers

Answer:

It has 13 sides.

Step-by-step explanation:

The equation for total interior angle is x = 180(n - 2)

fill it out and solve

1980 = 180(n - 2)

1980 = 180n - 360

2340 = 180n

n = 13

Can you help please, ASAP?

Answers

Q: -2,0
R: -1,4
S: 0,2

Help me please thanks

Answers

Given:

Triangle ABC and triangle DEF are similar triangles.

To find:

The proportion that can be used to find the length of segment DE.

Solution:

We know that the corresponding sides of similar triangles are proportional.

Triangle ABC and triangle DEF are similar triangles. So, their corresponding sides must be proportional.

[tex]\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}[/tex]

[tex]\dfrac{AB}{DE}=\dfrac{BC}{EF}[/tex]

[tex]\dfrac{4}{DE}=\dfrac{3}{9}[/tex]

[tex]\dfrac{4}{3}=\dfrac{DE}{9}[/tex]

Therefore, the correct option is A.

what is the measure of SPT?​

Answers

Answer:

Step-by-step explanation:

The Standard Penetration Test (SPT) is a widely used geotechnical test used to estimate soil strength. A SPT hammer drives a split barrel sampler at the bottom of a drive rod and recovers soil samples.

The total weight of the shape blocks on both sides of Michael's pan balance equals 30 grams. Circles weigh 5 grams, squares weigh 10 grams, and triangles weigh 3 grams. The right side has a circle and a square. How many triangles are on the left side?

Answers

Answer:

There would be 5 triangles on the other side

Step-by-step explanation:

If the right side has 1 circle and 1 square, that would mean that there is 5g+10g=15g weight on the right side

In total, there is 30g, and we already have 15

We can use the equation 15+3x=30, and by solving, the answer would be 5 triangles.

Hope this helps!

2. 5x2 + 16x - 84 = 0
Helppp please

Answers

Answer:

the x would equal 25 as 5x2 is 10 + 16x25 - 84 is 0.

Step-by-step explanation:

Answer:

2.8, –6

Step-by-step explanation:

The equation is already instandard form. Use the quadraticformula.5x2+16x−84=0x=−b±b2−4ac√2aSubstitute 5 for a, 16 for b,and −84 for c. Solve to getx=2.  8 or x=−  6.

helpppppppppppplppppppp​

Answers

Answer:

17 cm

Step-by-step explanation:

By Pythagoras Theorem

[tex]k = \sqrt{ {15}^{2} + {8}^{2} } \\ \\ k = \sqrt{ 225+ 64 } \\ \\ k = \sqrt{289} \\ \\ k = 17 \: cm[/tex]

Hi the answer is 17cm

Simplify:

-2(3x-1) + x(3x+2)

Answers

Answer:

-4x+3x power of 2 +2

Step-by-step explanation:

Answer:

3x² - 4x + 2

Step-by-step explanation:

distribute -2 into (3x - 1) and distribute x into (3x + 2)

=> -6x + 2 + 3x² + 2x

combine like terms

=> 3x² - 4x + 2

1,345,456,234,234,345,234,-1234,567,890=? My subsititue is being mean so we can not use calculatars and I do not like to cheat anyway but in this case (yes)

Answers

Answer:

1,345,456,232,999, 777,344

Step-by-step explanation:

1,345,456,23   4,   2   3    4,   3    4     5,   2    3      4,

                        -1    2   3     4,    5   6     7,   8    9     0        

1,345,456,23    2,  9   9     9,    7     7    7,   3   4     4      

So we write the ones under the ones, tens under the tens  starting from the right hand side.

The first numbers can be easily subtracted as 4 is greater than zero. Then comes 3 which is less than 9 so we borrow 1 digit from the left to right to make it 13 and subtract 9 from it and get a 4. Then we are left with 1 as we have already borrowed 1 digit. As 1 is less than 8 we again borrow 1 digit from the left to make it 11 and subtract 8 and get 3. So the next number is 4 as we have already borrowed 1 and it is less than 7 . Again we will borrow 1 digit from the left to make it 14 and subtract 7 to get a 7.

So the process continues until we get the answer.

pls help me with the answer​

Answers

Answer:

-27

5

10

-13

Step-by-step explanation:

-9*3=-27   -*+=-

-25/-5=5   -/-=+

7-(-3)=7+3=10  -(-)=+

-2+-11=-13   -+-=-


A pet store advertises
a 30% off sale or dog crates.
What is the regular price of a
large crate that costs $85.50
on sale?

Answers

Answer:

the answer is 1.99 I think im not sure I guessed

Step-by-step explanation:

M varies directly as n, and m=14 when n=7 a) Write an equation that relates m and n b) find m when n=16 c) find n when m=30

Answers

Answer:a)m =K n

b)m = 32

c)n=15

Step-by-step explanation:

M varies directly as n can be expressed mathematically as

m ∝ n

Introducing the constant of proportionality, K, we have that

m =K n

Now when m=14 and n=7, K becomes

14=K X 7

K=14/7 = 2

b) find m when n=16

m =K n

m = 2 x 16=32

c) find n when m=30

m =K n

30=2 x n

n=30/2 =15

Expression is formed using numbers, variables, and mathematical operations. The value of m, when the value of n is 16 is 32.

What is Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

As we know that the value of m is directly varying with n, therefore, we can write the relationship as,

[tex]m \propto n[/tex]

Now, in order to remove the proportionality, we will add a constant,

[tex]m = kn[/tex]

As the value of m and n is given as 14 and 7, substitute the values in order to get the value of the constant k,

[tex]m = kn\\14 = k(7)\\\dfrac{14}{7} = k\\k=2[/tex]

We know the value of the constant k is 2, therefore, the equation can be written as,

[tex]m=2n[/tex]

Substitute the value of n as 16, to get the value of m,

[tex]m=2n\\m=2(16)\\m=32[/tex]

Hence, the value of m, when the value of n is 16 is 32.

Learn more about Expression:

https://brainly.com/question/13947055

2. Simplify each expression.
6n + 3 + 2n
99-9-9
2p + 3p+ 6-p-3
2.25(14.3m + 6 + 2.7m)

Answers

Answer:

[tex]6n + 3 + 2n = 8n + 3[/tex]

[tex]99-9-9 = 81[/tex]

[tex]2p + 3p+ 6-p-3 = 4p + 3[/tex]

[tex]2.25(14.3m + 6 + 2.7m) = 38.25m + 15.5[/tex]

Please help me! This may be easy for some of you..

Answers

Answer:

9) 5

10) 5x+2

11) -1

12) -x+6


Please help me with this... figure out the missing part.

Answers

3/5 I the answer to this question!!

have another one that I need done ASAP please and thank u!!!

Answers

Answer:

1/3

Step-by-step explanation:

(-6,0) (-3,1)

1-0/ -3 - -6 = 1/3

.................................................................. help ,,,,,

Answers

Answer:

Possible answer: 5a/ -6

Step-by-step explanation:

Not 100% sure to be honest.

Write an expression for “Triple the sum of 33 and b”. *

Answers

Answer:

99+3b

Step-by-step explanation:

The original equation would be 3(33+b), but simplifying it would get 99+3b.

Megan and Devon are working together in science class to build a terrarium for an herb garden. The plan for the terrarium, with some dimensions in centimeters (cm), is shown here. What is the volume of the terrarium?

Answers

Answer:

48,000,000

Step-by-step explanation:

just multiply them all

10 minus what gives you 13.3

Answers

10 minus negative 3.3 gives you 13.3

HELPPPP ME FAST PLEASE

Answers

Answer:

B. 315 meters

Step-by-step explanation:

The length of the longer side of the lot on drawing = 6.3 cm

Given a scale of 1cm : 50 m

Let the length of the longer side be represented as x.

Therefore, the actual length of the longer side will be calculated as follows:

1:50 = 6.3:x

1/50 = 6.3/x

Cross multiply

x*1 = 50*6.3

x = 315

Actual length of the longer side of the lot = 315 meters

There are 60 calico cats at the animal shelter if this represents 30% of the cats in the shelter how many total cats are there

Answers

Answer: 200 cats in total

Step-by-step explanation:

60 calico cats represents 30% of the total cat population in the shelter.

That means that if we find 30% of the total number of cats, the number we will get is 60.

Assuming the total is x, representing this in equation form makes it:

x * 30% = 60

x = 60 / 30%

x = 200 cats in total

Giving brainlist to whoever answers

Answers

Answer:

84+ z =180

Step-by-step explanation:

42 x 2=84

84+ z =180

The measure of <E , the angle of elevation from point A to point B, is (3x+1)". The measure of <D.
the angle of depression from point B to pointA, is 2(x+8). Find the measure of each angle.
m<E = 22⁰, m<D = 30°
m<E = 15⁰, m<D=15°
m<E = 46°, m<D = 46°
m<E = 52⁰, m<D= 50°​

Answers

Answer:

last answer choice

Step-by-step explanation:

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