Is (1+cot^2(θ))sin^2(θ)=1 ?

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

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prove (1+cot^2(θ))sin^2(θ)=1

prove

(1 + cot^{2} (θ)) sin^{2} (θ) = 1

True

Solution steps

(1 + cot^{2} (θ)) sin^{2} (θ) = 1

Manipulating left side

(1 + cot^{2} (θ)) sin^{2} (θ)

Express with sin, cos

= cos^{2} (θ) + sin^{2} (θ)

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

1 - tan^{2} (x) = \frac{cos ( 2 x )}{cos ^{2} ( x )}

sin^{2} (- θ) + cos^{2} (- θ) = 1

\frac{cos ( θ )}{sin ( θ ) cot ( θ )} = 1

csc (u) - cot (u) = \frac{sin ( u )}{1 + cos ( u )}

csc (x) + cot (x) = \frac{sin ( x )}{1 - cos ( x )}

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