Trigonometry

Question

Verify the following identity: sin(α+β)+sin(α-β)=2sinαcosβ

Answer 1

sin (a + B) + sin (a - B) = 2 sin a Cos B

 

Use the sum/difference identities to make substitutions on the left-hand side.

 

sin a cos B + cos a sin B + sin a cos B - cos a sin B

 

Combine like terms.

 

2 sin a cos B