Question

sina_____=1/2(sin(a+b)+sin(a-b)).................is which of these......cosb, sinb, sina, cosa

Answer 1

cosb

Answer 2

Using sum and difference identities to expand the values in the 1/2:
\[(\sin a \cos b + \cos a \sin b)+(\sin a \cos b - \cos a \sin b)\]
Simplify:
\[2\sin a\cos b\]
Put it back in the equation:
\[\frac{1}{2}(2\sin a \cos b)\]
2's cancel:
\[\sin a \cos b\]
Therefore, \(\cos b\)!

Answer 3

thank u so much!