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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 sin^{2} (x) - 1

Rewrite using trig identities

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

cos (x) - sin^{2} (x) cos (x) = cos^{3} (x)

- tan (x) cos (x) = - sin (x)

sin (x) sin (x) = tan (x)

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