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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{2} (1 - cos (2 x))

Rewrite using trig identities

= sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

csc^{2} (x) tan^{2} (x) = \frac{1}{cos ^{2} ( x )}

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

cos (θ) = 2 cos^{2} (\frac{θ}{2}) - 1

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

cos (4 x) = 1 - 8 cos^{2} (x) + 8 cos^{4} (x)

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