mathematics(trignometri)

Question

show that (1+sin theta-cos theta/1+sin theta +cos theta)^2=1-cos theta/1+cos theta

Answer 1

It is too hard to write the whole derivation in this editor, but I will tell you how to do it.

For ease of typing I am going to write x instead of theta.

First multiply the expression on the left by (1+cos x)/sin x and show that the product = 1.

You will need to expand the numerator and use the identity sin² + cos² = 1.

That means the expression on the left is equal to (sin x)/(1+cos x)

It is then easy to show that [(sin x)/(1+cos x)]² = (1-cos x)/(1+cos x).

Remember sin² = 1-cos² = (1+cos)(1-cos)