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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Factor

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

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

Rewrite using trig identities

= 2 cos^{2} (w)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (b) + sin (b) tan (b) = sec (b)

2 sin (2 θ) (1 - 2 sin^{2} (θ)) = sin (4 θ)

cos^{2} (x) csc^{2} (x) = cot^{2} (x)

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

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