please help me prove the identity​

Answer:

[tex]\frac{1-\tan x }{1+\cot x}[/tex]

Step-by-step explanation:

Let [tex]\frac{\sin 2x+\cos 2x-1}{\sin 2x+\cos 2x + 1}[/tex], we proceed to prove the given identity by trigonometric and algebraic means:

1) [tex]\frac{\sin 2x+\cos 2x-1}{\sin 2x+\cos 2x + 1}[/tex] Given

2) [tex]\frac{2\cdot \sin x \cdot \cos x +\cos ^{2}x - \sin^{2}x-1}{2\cdot \sin x \cdot \cos x +\cos ^{2}x - \sin^{2}x+1}[/tex] [tex]\sin 2x = 2\cdot \sin x \cdot \cos x[/tex]/[tex]\cos 2x = \cos^{2}x - \sin^{2}x[/tex]

3) [tex]\frac{2\cdot \sin x \cdot \cos x -\sin^{2}x-(1-\cos^{2}x)}{2\cdot \sin x\cdot \cos x +\cos^{2}x+(1-\sin^{2}x)}[/tex] Commutative, associative and distributive properties/[tex]-a = (-1)\cdot a[/tex]

4) [tex]\frac{2\cdot \sin x \cdot \cos x -2\cdot \sin^{2}x}{2\cdot \sin x \cdot \cos x +2\cdot \cos^{2}x}[/tex] [tex]\sin^{2}x + \cos^{2}x = 1[/tex]

5) [tex]\frac{(2\cdot \sin x)\cdot (\cos x-\sin x)}{(2\cdot \cos x)\cdot (\sin x +\cos x)}[/tex] Distributive and associative properties.

6) [tex]\frac{\sin x\cdot (\cos x-\sin x)}{\cos x\cdot (\sin x +\cos x)}[/tex] Existence of multiplicative inverse/Commutative and modulative properties.

7) [tex]\frac{\frac{\cos x -\sin x}{\cos x} }{\frac{\sin x + \cos x}{\sin x} }[/tex] [tex]\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}[/tex]

8) [tex]\frac{\frac{\cos x}{\cos x}-\frac{\sin x}{\cos x} }{\frac{\sin x}{\sin x}+\frac{\cos x}{\sin x} }[/tex] [tex]\frac{x+y}{w} = \frac{x}{w} + \frac{y}{w}[/tex]

9) [tex]\frac{1-\tan x }{1+\cot x}[/tex] Existence of multiplicative inverse/[tex]\tan x = \frac{\sin x}{\cos x}[/tex]/[tex]\cot x = \frac{\cos x}{\sin x}[/tex]/Result

Fay has a lemonade stand.
She spends £42 on ingredients.
She sells each glass of lemonade for £1.50.
If she sells 30 glasses of lemonade, what is her total profit?

2x + 5y = 6
find the x-intercept of the line

A music store has 5 guitars for sale. Each guitar has 6 strings. The manager wants to replace all the strings. How many new strings does he need?

Write the following in standard form:
Write
A = 4
B = 2
C = 7

1/1
Proportion
ains 12 marbles. The marbles are either red or blue. If th
1: 2, how many of each colour are there in the bag?

I need help with this ​

Can you please not sit on my eggplant Because if 6 inches plus 6 inches is not 3 inches but it would be 12 inches then why would it be 12 inches if it wasn’t 3 inches?

1:
Segment EG is an angle bisector of angle FGH. Abraham wrote a proof to show
that triangle HEG is congruent to triangle FEG.
2
3
5
6
G
1. Side EG is congruent to side EG because they're the same segment.
2. Angle EGH is congruent to angle EGF because segment EG is an angle
bisector of angle FGH.
3. Angle H EG is congruent to angle FEG because segment EG is an angle
bisector of angle FGH.

proportion multiple choice​

Bella measured the heights of her corn stalks in centimeters. The heights are 81, 88, 69, 65, 87.
What is the mean height of Bella's corn stalks?
A. 69 cm
B. 75 cm
C. 78 cm
D. 80 cm
E. 81 cm

What is a formula for the nth term of the given sequence? 160,200,250

Find the volume of a cylinder with a height of 7 cm and a radius of 3 cm.

A. 21 / cm3

B. 63 71 cm

C. 147 cm

D. 42 71 cm​

The diameter of a circle is 16 yards. What is the circle's area?
d=16 yd
Use 3.14 for n.

The CEO of a cell-phone company has recently noticed a 26% sales decrease in the month of July compared to June. Let n represent June’s sales. If y represents July’s sales, which equation can be used to determine the sales in July?

What is the measurement of the unknown angle?
70°
2
127
146°

What is the slope of the line y=8?

To ride an amusement park ride, your height must be at or above the line on the sign. For each set of information, write an integer that represents a person's height relative to the line on the sign and type yes or no as to whether they can ride the ride.

If MP=6x-5,QR=3x+1, and RN=6, what is QN

7 points
1. Original points (1,3), (3,2), and (4.2) are drawn on a graph and transformed to points
(-1,3), (-3,2), and (-4,2). Which rule describes the transformation performed? *
(x,y) -> (-x, y) because the triangle was reflected over the y-axis
(x,y) -> (x,-y) because the triangle was reflected over the x-axis
(x,y) -> (x, y - 2) because the triangle was translated 2 units down
O
(x,y) -> (x, y-6) because the triangle was translated 6 units down

2s + (-4s) simplify

NEED HELP PLSS!!!



pls dont answer if you dont know

Solve 3(x − 4) = 12x
x=?

help for brainlest what can be use ti

100 POINTS. HELP ASAP !!! PLEASE PLEASE

Not drawn
accurately
AB is parallel to CD.
LMN and PMQ are straight lines.
MQ = MN
B
Work out the value of x. *
(3 Points)
Diagram not drawn accurately.
-D
The value must be a number

What is the answer to this.

Thomas and Tina share a cake. Thomas eats 12.5% of the cake. Tina eats
2
176 of the cake. The fraction of cake remaining is "b/c". What is the value of
b? *
Your answer
This is a required question
O​

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Solve each equation for the
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what is the other endpoint of a segment with one endpoint at(-3, 8) and the midpoint at (7, 1)?​