Is (csc^2(x)-1)sin(x)=cot^2(x)sin(x) ?

The answer to whether (csc^2(x)-1)sin(x)=cot^2(x)sin(x) is True

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prove (csc^2(x)-1)sin(x)=cot^2(x)sin(x)

prove

(csc^{2} (x) - 1) sin (x) = cot^{2} (x) sin (x)

True

Solution steps

(csc^{2} (x) - 1) sin (x) = cot^{2} (x) sin (x)

Manipulating left side

(csc^{2} (x) - 1) sin (x)

Rewrite using trig identities

= cot^{2} (x) sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{3 sin ^{2} ( t )}{tan ^{2} ( t )} = 3 cos^{2} (t)

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

\frac{sin ( 3 θ )}{sin ( θ )} = 3 - 4 sin^{2} (θ)

tan (π - θ) = tan (θ)

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