How do you simplify -1/(cos2theta)+tan2theta−1cos2θ+tan2θ using the double angle identities?

1 Answer
P dilip_k
Jun 11, 2016

=((sintheta-costheta)/(costheta+sintheta))(sinθ−cosθcosθ+sinθ)

Explanation:

-1/(cos2theta)+tan2theta−1cos2θ+tan2θ

=-1/(cos2theta)+(sin2theta)/(cos2theta=−1cos2θ+sin2θcos2θ

=-(1-sin2theta)/(cos2theta)=−1−sin2θcos2θ

=-((1-sin2theta)/(cos2theta))=−(1−sin2θcos2θ)

=-((cos^2theta+sin^2theta-2sinthetacostheta)/(cos^2theta-sin^2theta))=−(cos2θ+sin2θ−2sinθcosθcos2θ−sin2θ)

=-((costheta-sintheta)cancel((costheta-sintheta)))/((costheta+sintheta)cancel((costheta-sintheta)))

=-((costheta-sintheta)/(costheta+sintheta))

=((sintheta-costheta)/(costheta+sintheta))

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