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18 August, 06:23

Verify the identity and explain how cot (x - pi/2) = - tan x

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  1. 18 August, 08:34
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    First, let's recall some usefull information:

    - cot (x) = 1/tg (x) = cos (x) / sin (x)

    - tan (x) = sin (x) / cos (x)

    We also know that:

    - cos (x - pi/2) = sin (x)

    - sin (x - pi/2) = - cos (x)

    Now we can use those relationships and get:

    cot (x - pi/2) = cos (x - pi/2) / sin (x - pi/2) = sin (x) / -cos (x) = - tan (x)

    So we have verified the identity, and explained step by step why the identity is true.
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