Simplify #(sintheta + cos2theta - 1)/(costheta-sin2theta)#?

Answer is #tantheta# but I don't get how to get there...

1 Answer
Noah G
Apr 5, 2018

Please see below.

Explanation:

Recall that #cos(2theta) = 1 - 2sin^2theta# and #sin(2theta) = 2sinthetacostheta#.

#=(sintheta + 1 - 2sin^2theta - 1)/(costheta - 2sinthetacostheta)#

#=(sintheta - 2sin^2theta)/(costheta - 2sinthetacostheta)#

#=(sintheta(1 - 2sintheta))/(costheta(1 - 2sintheta))#

#=sintheta/costheta#

#=tantheta#

Hopefully this helps!

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