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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= csc^{2} (x) + 1

We showed that the two sides could take the same form

\Rightarrow True

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

sin (θ) + cos (θ) = 2 sin (θ + 4 5^{\circ})

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

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

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

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