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.