Is cot^2(θ)(1+tan^2(θ))=csc^2(θ) ?

The answer to whether cot^2(θ)(1+tan^2(θ))=csc^2(θ) is True

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prove cot^2(θ)(1+tan^2(θ))=csc^2(θ)

prove

cot^{2} (θ) (1 + tan^{2} (θ)) = csc^{2} (θ)

True

Solution steps

cot^{2} (θ) (1 + tan^{2} (θ)) = csc^{2} (θ)

Manipulating left side

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

= \frac{1}{sin ^{2} ( θ )}

Rewrite using trig identities

csc^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

sin (2 A) = 2 sin (A)

tan (θ) cos (θ) csc (θ) = 1

sin^{2} (x + \frac{π}{4}) - cos^{2} (x - \frac{π}{4}) = 0

tan^{2} (u) - sin^{2} (u) = tan^{2} (u) sin^{2} (u)

cos (x) - cos (x) sin^{2} (x) = cos^{3} (x)

Is cot^2(θ)(1+tan^2(θ))=csc^2(θ) ?
The answer to whether cot^2(θ)(1+tan^2(θ))=csc^2(θ) is True