Write cot^(2) x (1+tan^(2) x) Then simplify the expression so no quotients appear

asked Jun 15, 2022 35.0k views

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Write

Then simplify the expression so no quotients appear

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Explanation:

${ \cot^(2)x}(1 + \tan^(2)x) \\ = (1)/( \tan^(2)x) (1 + \tan^(2)x)$

$= (1)/( \tan^(2)x ) + 1$

$= ( \cos^(2) x )/( \sin^(2)x ) + 1 = ( \cos^(2)x + \sin^(2)x)/( \sin^(2) x )$

$= (1)/( \sin^(2)x ) = \csc^(2) x$

Amir Doreh answered Jun 20, 2022

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