Is sin(θ)(1+cot^2(θ))=csc(θ) ?

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

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prove sin(θ)(1+cot^2(θ))=csc(θ)

prove

sin (θ) (1 + cot^{2} (θ)) = csc (θ)

True

Solution steps

sin (θ) (1 + cot^{2} (θ)) = csc (θ)

Manipulating left side

sin (θ) (1 + cot^{2} (θ))

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{sin ( θ )}

Rewrite using trig identities

csc (θ)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) - sin (x) = csc (x) cot (x)

5 + cot^{2} (x) = 4 + csc^{2} (x)

\frac{1}{2} sin (2 x) = \frac{tan ( x )}{1 + tan ^{2} ( x )}

sin^{2} (2 x) = \frac{1 - cos ( 4 x )}{2}

cot (2 θ) = \frac{csc ( θ ) - 2 sin ( θ )}{2 cos ( θ )}

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