How do you verify the identity $sec^2xcotx-cotx=tanx$ ?

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Answer 1 · 2017-01-17T20:18:24

see below

Left Hand Side:

$sec^2x cot x - cot x=cotx(sec^2x-1)$

Use identity: $1+tan^2x=sec^2x$

$=cotxtan^2x$

$=cosx/sinx * sin^2x/cos^2x$

$=cancelcosx/cancelsinx * sin^cancel2x/cos^cancel2x$

$=sinx/cosx$

$=tanx$

$:.=$ Right Hand Side

How do you verify the identity sec^2xcotx-cotx=tanxsec^2xcotx-cotx=tanx?