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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sin^{4} (x) - 2 sin^{2} (x)

Factor

sin^{4} (x) - 2 sin^{2} (x) : sin^{2} (x) (sin^{2} (x) - 2)

= (- 2 + sin^{2} (x)) sin^{2} (x)

Rewrite using trig identities

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

Expand

(- 1 - cos^{2} (x)) (1 - cos^{2} (x)) : - 1 + cos^{4} (x)

= - 1 + cos^{4} (x)

= cos^{4} (x) - 1

We showed that the two sides could take the same form

\Rightarrow True

cot^{4} (a) = \frac{cos ^{4} ( a )}{sin ^{4} ( a )}

1 + sec^{2} (x) sin (x) = sec^{2} (x)

3 sin (x) = cos (x)

\frac{cot ( x )}{csc ( x ) - sin ( x )} = sec (x)

sin (x) = 5 cos (x)

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