SOLUTION: Prove the identity sin(pi/2-x) cot(pi/2+x)= -sinx

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Question 1012333: Prove the identity sin(pi/2-x) cot(pi/2+x)= -sinx
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+sin%28pi%2F2-x%29+cot%28pi%2F2%2Bx%29=+-sin%28x%29+
using Cofunctions Identities, we have:

sin%28pi%2F2-x%29+=cos%28x%29 and
cot%28pi%2F2%2Bx%29=-tan%28x%29
so, cos%28x%29+%28-tan%28x%29%29=+-sin%28x%29 ...since -tan%28x%29=-sin%28x%29%2Fcos%28x%29, we have
cos%28x%29+%28-sin%28x%29%2Fcos%28x%29%29=+-sin%28x+%29
cross%28cos%28x%29+%29%28-sin%28x%29%2Fcross%28cos%28x%29%29%29=+-sin%28x%29
-sin%28x%29=+-sin%28x%29+