Which set of steps can be used to prove the sine sum identity, sine of open paren x plus y close paren is equal to sine x plus cosine x ?
Answer
A
Use the supplementary relationship between sine and cosine to rewrite sine of open paren x plus y close paren as cosine of open paren pi over 2 minus open paren x plus y close paren close paren . Apply the cosine sum identity. Then simplify using sine of negative y is equal to negative sine times y and cosine of negative y is equal to cosine of y .
B
Use the complementary relationship between sine and cosine to rewrite sine of open paren x plus y close paren as cosine of open paren pi over 2 minus open paren x plus y close paren close paren . Apply the cosine sum identity. Then simplify using sine of negative y is equal to sine of y and cosine of negative y is equal to negative cosine times y .
C
Use the supplementary relationship between sine and cosine to rewrite sine of open paren x plus y close paren as cosine of open paren pi over 2 minus open paren x plus y close paren close paren . Apply the cosine sum identity. Then simplify using sine of negative y is equal to sine of y and cosine of negative y is equal to negative cosine times y .
D
Use the complementary relationship between sine and cosine to rewrite sine of open paren x plus y close paren as cosine of open paren pi over 2 minus open paren x plus y close paren close paren . Apply the cosine sum identity. Then simplify using sine of negative y is equal to negative sine times y and cosine of negative y is equal to cosine of y .