How do you verify $secx-cosx=sinx/cotx$ ?

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Answer 1 · 2016-04-24T16:24:41

Use the following identities:

$secx = 1/cosx$

$cotx = cosx/sinx$

$1/cosx - cosx= sinx/(cosx/sinx)$

$(1 - (cosx)(cosx))/cosx = ((sinx)(sinx))/cosx$

Applying the pythagorean identity $1 - cos^2x = sin^2x$ :

$sin^2x/cosx = sin^2x/cosx$

Thus, your identity is proved!

How do you verify secx-cosx=sinx/cotxsecx-cosx=sinx/cotx?