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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