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Valentino Hamilton
6 March, 04:22
Verify the identity.
tan (x+pi/2) = - cot x
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Kaya
6 March, 04:38
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Work the left side
tan (x + pi/2) = sin (x+pi/2) / cos (x+pi/2)
Now you should know that sin (x+pi/2) = cos (x) and cos (x+pi/2) = - sin (x)
if you do not know that you can obtain from the sin (x+y) and cos (x+y) formulaes doing y = pi/2.
Continue:
sin (x+pi/2) / cos (x+pi/2) = cos (x) / [ - sin (x) ] = - 1 / tan (x) = - cot (x).
Then, we have obtained the right side from the left side, and the identity is verified.
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