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16 June, 21:01

Verify the identity.

tan (x+pi/2) = - cot x

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  1. 16 June, 21:17
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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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