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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 cos^{2} (w) - 1

Rewrite using trig identities

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

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

We showed that the two sides could take the same form

\Rightarrow True

sin (x) (1 + cot^{2} (x)) = csc^{2} (x)

(1 - cos (x)) (1 + sec (x)) = - sin (x)

4 cot (x) = cot (x) sin^{2} (x)

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

cos^{2} (7 x) - sin^{2} (7 x) = cos (14 x)

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