For what values of $x$ does $sqrt((1-sinx)/(1+sinx))=secx-tanx$ hold?

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Answer 1 · 2017-04-16T16:00:16

Identity holds for all values of $x$ , irrespective of quadrant.

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

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

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

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

= $(1-sinx)/cosx$

= $1/cosx-sinx/cosx$

= $secx-tanx$

Above is an identity and hence it holds for all values of $x$ i.e. for any quadrant.

For what values of xx does sqrt((1-sinx)/(1+sinx))=secx-tanxsqrt((1-sinx)/(1+sinx))=secx-tanx hold?