Prove that each of these equations is an identity.

Question

A) (1 + sinx + cos x)/(1 + sinx + cosx)=(1 + cosx)/sinx

B) (1 + sinx + cosx)/(1 - sinx + cosx)= (1 + sin x)/cosx

Please and thankyou!

Answer 1

you must have a typo in A since the left side equals 1

for B
multiply the left side by (1+sinx-cosx)/(1+sinx-cosx)
which after collecting like terms, and reducing comes to the right side.
A key simplification is the sequence of terms
1 ....+sin^2x... - cos^2x

which reduces to 2sin^2x

I am sure a similar step will work for A) after you find your typo

Answer 2

Ok thanks, I did make a typo my bad.