How do you simplify $(1+sin2x+cos2x)/(1+sin2x-cos2x)$ ?

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Answer 1 · 2016-09-29T05:08:23

$(1+sin2x+cos2x)/(1+sin2x-cos2x)$

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

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

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

$=cotx$

How do you simplify (1+sin2x+cos2x)/(1+sin2x-cos2x)(1+sin2x+cos2x)/(1+sin2x-cos2x)?