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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

1 - cos^{2} (θ) = sin^{2} (θ)

tan (\frac{π}{4} - θ) = \frac{cos ( θ ) - sin ( θ )}{cos ( θ ) + sin ( θ )}

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

\frac{1 + sec ^{2} ( θ )}{sec ^{2} ( θ )} = 1 + cos^{2} (θ)

cos (2 a + a) = - 3 cos (a) + 4 cos^{3} (a)

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