Question

Verify the identity:
sin(A + B)
sin( A B)
tan(-4) + tan(B)
tan(4) tan(B)

Answer 1

i think is the answer is

sin(A+B)

Answer 2

Numerator:

• sin (A + B) = sin A cos B + cos A sin B

Divide by cos A cos B:

• sin A /cos A + sin B /cos B = tan A + tan B

Denominator:

• sin (A - B) = sin A cos B - cos A sin B

Divide by cos A cos B:

• sin A /cos A - sin B /cos B = tan A - tan B

Connect all bits together to get:

• sin(A + B) / sin(A - B) = (tan A + tan B) / (tan A - tan B)