Verify help, please help me

Question

sin(x+y)·sin(x-y)=sin²x-sin²y

i know I’m doing something wrong because i keep getting to sin²x·cos²y-sin²y·cos²x

Answer 1

You are on the right track, you just didn't go far enough.

From where you were:

sin²x·cos²y - sin²y·cos²x [Now use cos²y = 1 - sin²y and cos²x = 1 - sin²x replace cos²y and cos²x:

sin²x·(1 - sin²y) - sin²y·(1 - sin²x) [then distribute to get:

sin²x - sin²x·sin²y - sin²y + sin²x·sin²y [notice now that there are "+" and "-" versions of sin²x·sin²y that cancel to get:

sin²x - sin²y