If Sin A = Sin B, then is Sin(A/2) = Sin(B/2)?

Question

Please Explain clearly with valid Proofs.

if its true then, Will it be true for the other trigonometric functions?

Answer 1

The statement is FALSE!

Here is a counter example:

Sin(60) = sin(120) = sqrt(3)/2 because the sine function is positive in quadrants 1 and 2.

But

sin(60/2) = sin(30) = 1/2 while sin(120/2) = sin(60) = sqrt(3)/2