If $y=(sinx-cosx)/(sinx+cosx)$ , then find the value of $1+y^2$ ?

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Answer 1 · 2017-05-13T04:39:40

$1+y^2=2/(1+sin2x)$

As $y=(sinx-cosx)/(sinx+cosx)$

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

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

$=(2sin^2x+2cos^2x)/(sin^2x+cos^2x+2sinxcosx)$

$=2/(1+sin2x)$

If y=(sinx-cosx)/(sinx+cosx)y=(sinx-cosx)/(sinx+cosx), then find the value of 1+y^21+y^2?