Solve the equation #(1+sinx)/(1-sinx)=2sec^2x+2secxtanx-1#?

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Answer 1 · 2018-01-14T09:03:01

It is an identity.

Equation is an identity. Proof is given below.

#(1+sinx)/(1-sinx)#

= #(1+sinx)^2/((1-sinx)(1+sinx))#

= #(1+2sinx+sin^2x)/(1-sin^2x)#

= #(1+2sinx+1-cos^2x)/cos^2x#

= #2/cos^2x+2sinx/cos^2x-1#

= #2sec^2x+2*1/cosx*sinx/cosx-1#

= #2sec^2x+2secxtanx-1#