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.

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

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

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

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

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

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

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

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