SOLUTION: Verify the identity by transforming the left-hand side into the right-hand side. cot(-x) * cos(-x) + sin(-x) = -csc(x)

Algebra ->  Trigonometry-basics -> SOLUTION: Verify the identity by transforming the left-hand side into the right-hand side. cot(-x) * cos(-x) + sin(-x) = -csc(x)      Log On


   

Question 985645: Verify the identity by transforming the left-hand side into the right-hand side.
cot(-x) * cos(-x) + sin(-x) = -csc(x)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
highlight_green%28cot%28-x%29+%2A+cos%28-x%29+%2B+sin%28-x%29+=+-csc%28x%29%29

Necessary to understand cos%28-x%29=cos%28x%29 and sin%28-x%29=-sin%28x%29.
If unsure how, check on the unit circle.

L.H.S., %28cos%28-x%29%2Fsin%28-x%29%29cos%28-x%29%2Bsin%28-x%29
%28cos%28x%29%2F%28-sin%28x%29%29%29cos%28x%29%2B%28-sin%28x%29%29
-%28cos%5E2%28x%29%2Fsin%28x%29%2Bsin%28x%29%29
-%28%28cos%5E2%28x%29%2Bsin%5E2%28x%29%29%2F%28sin%28x%29%29%29
-%281%2Fsin%28x%29%29
and by definition
-csc%28x%29