Is (1+cot^2(θ))tan^2(θ)=sec^2(θ) ?

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

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prove (1+cot^2(θ))tan^2(θ)=sec^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

(1 + cot^{2} (θ)) tan^{2} (θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ^{2} ( θ )}

Rewrite using trig identities

sec^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

sin (a) + cos (a) = \frac{1 + tan ( a )}{sec ( a )}

(cos (x))^{3} = cos^{3} (x)

cot (θ) = sec (θ) csc (θ) - tan (θ)

sin^{2} (β) csc^{2} (β) - sin^{2} (β) = cos^{2} (β)

(sin (θ) + 1) (sin (θ) - 1) = - cos^{2} (θ)

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