Prove that $secx-tanx=sqrt((1-sinx)/(1+sinx)$ ?

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Answer 1 · 2017-04-07T12:57:14

Please see below.

$secx-tanx$

= $1/cosx-sinx/cosx$

= $(1-sinx)/cosx$

= $sqrt((1-sinx)^2)/(sqrt(cos^2x))$

= $sqrt((1-sinx)^2)/(sqrt(1-sin^2x))$

= $sqrt((1-sinx)^2/(1-sin^2x))$

= $sqrt((1-sinx)^2/((1+sinx)(1-sinx))$

= $sqrt((1-sinx)/(1+sinx)$

Prove that secx-tanx=sqrt((1-sinx)/(1+sinx)secx-tanx=sqrt((1-sinx)/(1+sinx)?