Can someone help me solve this trigonometry proof?

Question

The proof is:

(sin x + cos x) / (1 – cos x) = tanx.

I've been trying to solve it, but I keep getting stuck. Can someone help me PLEASE?!

Answer 1

Check the problem statement . The equation is in error.

Answer 2

In proving trig. identities, you will not transfer/transpose any expression
(sin x + cos x)/(1 - cos x) = tan x
but instead of trying hard to prove this, why not find a counterexample?

Let x = 45
(sin 45 + cos 45)/(1 - cos 45) = tan 45
Now sin 45 = √2/2
cos 45 = √2/2
tan 45 = 1

(√2/2 + √2/2)/(1 - √2/2) = 1
(2√2/2)/[(2 - √2)/2] = 1
2√2/(2 - √2) = 1
2√2 = 2 - √2
2 = 2√2 + √2
2 = 3√2
√2 = 2/3
But √2 = 1.4142135627.... therefore, a contradiction.

(sin x + cos x)/(1 - cos x) = tan x is not an identity to be proven (true for all real values of x) but a mere trigonometric equation, which is only true for certain value/s of x.

^_^

Answer 3

They are not equal. When x=0, tan(0)=0. But since cos(0)=1. the left side is undefined at x=0.

Answer 4

For x = 90 degrees,
the right side is infinite, the left side is 1.

Answer 5

(sin x + cos x)=(1-cos x)
2cos x=1-sin x

Answer 6

This is not correct. The left side is not equal to tan(x). Substitute a value for x and test it.

Answer 7

Go to www.artofproblemsolving.com, register, and post your question in the appropriate forum. People there can help you a lot.

Answer 8

using this
sin x=2t/(1+t^2)
cos x=(1-t^2)/(1+t^2)
tan x =2t/(1-t^2)
WHERE t = tan (x/2)

Answer 9

(sin A cos B + cos A sin B)/(cos A cos B - sin A sin B) Divide the two numerator and denominator with the aid of cos A cos B: (sin A/cos A+ sin B/cos B)/(a million - sin A sin B/(cos A cos B)) Simplify: (tan A + tan B)/(a million - tan A tan B) And we are finished.

Answer 10

It does not work. Did you get all the signs right when you posted?