Simplify $(1+cos2A+sin2A)/(1-cos2A+sin2A)$ ?

Question

9736 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-18T07:29:22

Please see below.

$(1+cos2A+sin2A)/(1-cos2A+sin2A)$

Now $sin2A=2sinAcosA$ and $cos2A=2cos^2A-1=1-2sin^2A$

Hence $(1+cos2A+sin2A)/(1-cos2A+sin2A)$

= $(1+2cos^2A-1+2sinAcosA)/(1-(1-2sin^2A)+2sinAcosA)$

= $(1+2cos^2A-1+2sinAcosA)/(1-1+2sin^2A+2sinAcosA)$

= $(2cos^2A+2sinAcosA)/(2sin^2A+2sinAcosA)$

= $(2cosA(cosA+sinA))/(2sinA(sinA+cosA))$

= $(2cosA)/(2sinA)$

= $cotA$

Simplify (1+cos2A+sin2A)/(1-cos2A+sin2A)(1+cos2A+sin2A)/(1-cos2A+sin2A)?