SOLUTION: Prove that tan(pi/2+x)=-cotx

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Question 196590: Prove that tan(pi/2+x)=-cotx
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28pi%2F2%2Bx%29=-cot%28x%29 Start with the given equation.


Note: I'm ONLY manipulating the left side.


sin%28pi%2F2%2Bx%29%2Fcos%28pi%2F2%2Bx%29=-cot%28x%29 Use the identity tan%28x%29=sin%28x%29%2Fcos%28x%29


%28sin%28pi%2F2%29cos%28x%29%2Bcos%28pi%2F2%29sin%28x%29%29%2F%28cos%28pi%2F2%29cos%28x%29-sin%28pi%2F2%29sin%28x%29%29=-cot%28x%29 Expand

Note: sin%28A%2BB%29=sin%28A%29cos%28B%29%2Bcos%28A%29sin%28B%29 and cos%28A%2BB%29=cos%28A%29cos%28B%29-sin%28A%29sin%28B%29


%28%281%29cos%28x%29%2B%280%29sin%28x%29%29%2F%28%280%29cos%28x%29-%281%29sin%28x%29%29=-cot%28x%29 Evaluate the sine of pi%2F2 to get 1. Evaluate the cosine of pi%2F2 to get 0


%28cos%28x%29%2B0%29%2F%280-sin%28x%29%29=-cot%28x%29 Multiply


%28cos%28x%29%29%2F%28-sin%28x%29%29=-cot%28x%29 Simplify


-cot%28x%29=-cot%28x%29 Use the identity cot%28x%29=1%2Ftan%28x%29=cos%28x%29%2Fsin%28x%29


So this verifies the identity tan%28pi%2F2%2Bx%29=-cot%28x%29