Is (csc^4(x)-1)/(cot^2(x))=2+cot^2(x) ?

The answer to whether (csc^4(x)-1)/(cot^2(x))=2+cot^2(x) is True

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prove (csc^4(x)-1)/(cot^2(x))=2+cot^2(x)

prove

\frac{csc ^{4} ( x ) - 1}{cot ^{2} ( x )} = 2 + cot^{2} (x)

True

Solution steps

\frac{csc ^{4} ( x ) - 1}{cot ^{2} ( x )} = 2 + cot^{2} (x)

Manipulating left side

\frac{csc ^{4} ( x ) - 1}{cot ^{2} ( x )}

Rewrite using trig identities

= cot^{2} (x) + 2

= 2 + cot^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (arcsin (x) + arccos (x)) = 1

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

(sec (5 x) - 1) (sec (5 x) - 1) = tan^{2} (5 x)

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

cot (x) + tan (x) = sec (x) \cdot csc (x)

Is (csc^4(x)-1)/(cot^2(x))=2+cot^2(x) ?
The answer to whether (csc^4(x)-1)/(cot^2(x))=2+cot^2(x) is True