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

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

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

prove

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

True

Solution steps

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

Manipulating left side

1 - 2 cos^{2} (x)

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

sin (2 A) = 2 sin (A) cos (A)

tan (A - B) = sin (A - B) sec (A - B)

cot^{2} (θ) (1 - cos^{2} (θ)) = cos^{2} (θ)

sin (\frac{π}{3} + x) - cos (\frac{π}{6} + x) = sin (x)

csc (2 x) - cot (2 x) = tan (x)

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