SOLUTION: Simplify the following: sin (90° + x) sin (180° + x) + cos (90° + x) cos (180° – x)

Algebra ->  Trigonometry-basics -> SOLUTION: Simplify the following: sin (90° + x) sin (180° + x) + cos (90° + x) cos (180° – x)      Log On


   

Question 476923: Simplify the following:
sin (90° + x) sin (180° + x) + cos (90° + x) cos (180° – x)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
cos%2890%5Eo+%2B+x%29+=+-sinx
cos%28180%5Eo+-+x%29+=+-cosx
sin%28180%5Eo+%2B+x%29+=+-sinx
sin%2890%5Eo+%2B+x%29+=+cosx
==>sin (90° + x) sin (180° + x) + cos (90° + x) cos (180° – x) =
cosx*-sinx + -sinx*-cosx = -sinx*cosx + sinx*cosx = 0.