Is cot^2(x)csc^2(x)-cot^2(x)=cot^4(x) ?

The answer to whether cot^2(x)csc^2(x)-cot^2(x)=cot^4(x) is True

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prove cot^2(x)csc^2(x)-cot^2(x)=cot^4(x)

prove

cot^{2} (x) csc^{2} (x) - cot^{2} (x) = cot^{4} (x)

True

Solution steps

cot^{2} (x) csc^{2} (x) - cot^{2} (x) = cot^{4} (x)

Manipulating left side

cot^{2} (x) csc^{2} (x) - cot^{2} (x)

Rewrite using trig identities

= cot^{4} (x)

We showed that the two sides could take the same form

\Rightarrow True

arcsin (x) = csc (x)

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

(1 - sin (x)) (1 + csc (x)) = cos (x) cot (x)

\frac{1}{cos ( x )} = \frac{tan ( x )}{sin ( x )}

cos^{4} (A) - sin^{4} (A) = cos (2 A)

Is cot^2(x)csc^2(x)-cot^2(x)=cot^4(x) ?
The answer to whether cot^2(x)csc^2(x)-cot^2(x)=cot^4(x) is True