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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Factor

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

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

Rewrite using trig identities

= 2 cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (x) 2 sin (x) = sin (2 x)

\frac{csc ( a )}{csc ( a ) - sin ( a )} = sec^{2} (a)

sec^{2} (x) - sin^{2} (x) \cdot sec^{2} (x) = 1

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

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