SOLUTION: verify the identity cot(theta+pi/2)=-tan(theta)

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Question 981787: verify the identity
cot(theta+pi/2)=-tan(theta)
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!

1.  cot%28theta%2Bpi%2F2%29 = cos%28theta%2Bpi%2F2%29%2Fsin%28theta%2Bpi%2F2%29.

2.  cos%28theta%2Bpi%2F2%29 =     (apply the formula for cosines of the sum of angles,  see the lesson  Addition and subtraction formulas  in this site,  or any textbook on Trigonometry)
                        = cos%28theta%29.cos%28pi%2F2%29 - sin%28theta%29.sin%28pi%2F2%29 = cos%28theta%29.0%29 - sin%28theta%29.1 = -sin%28theta%29.

3.  sin%28theta%2Bpi%2F2%29 =     (apply the formula for sines of the sum of angles,  see the same lesson  Addition and subtraction formulas  in this site,  or any textbook on Trigonometry)
                        = sin%28theta%29.cos%28pi%2F2%29 + cos%28theta%29.sin%28pi%2F2%29 = sin%28theta%29.0%29 + cos%28theta%29.1 = cos%28theta%29.

Hence,  cot%28theta%2Bpi%2F2%29 = cos%28theta%2Bpi%2F2%29%2Fsin%28theta%2Bpi%2F2%29 = -sin%28theta%29%2Fcos%28theta%29 = -tan%28theta%29.

Conclusion.  The identity  cot%28theta%2Bpi%2F2%29 = -tan%28theta%29  which was proposed you to verify,  is true.