Is (1-cos^4(x))/(sin^2(x))=1+cos^2(x) ?

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

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prove (1-cos^4(x))/(sin^2(x))=1+cos^2(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1 - cos ^{4} ( x )}{sin ^{2} ( x )}

Rewrite using trig identities

= cos^{2} (x) + 1

= 1 + cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

2 cot^{2} (A) sin^{2} (A) = 1 + cos (2 A)

sin (x) + cos (x) = cos (x) (1 + tan (x))

\frac{sin ( x )}{sin ( 2 x )} = \frac{1}{2 cos ( x )}

cot (θ) sec^{2} (θ) - cot (θ) = tan (θ)

2 cos (x - \frac{π}{4}) = cos (x) + sin (x)

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