What is cot^2(θ)(1+tan^2(θ)) ?

The solution to cot^2(θ)(1+tan^2(θ)) is csc^2(θ)

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simplify cot^2(θ)(1+tan^2(θ))

simplify

cot^{2} (θ) (1 + tan^{2} (θ))

csc^{2} (θ)

Solution steps

cot^{2} (θ) (1 + tan^{2} (θ))

Express with sin, cos

= \frac{cos ^{2} ( θ ) + sin ^{2} ( θ )}{sin ^{2} ( θ )}

Rewrite using trig identities

= csc^{2} (θ)

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\frac{tan ( θ )}{sec ( θ )}

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\frac{x ^{8}}{5 x ^{3}}