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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cot^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

\frac{1}{cos ^{3} ( x )} = sec^{3} (x)

sin (x) + cot (x) (cos (x)) = csc (x)

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

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