Is sin^2(2x)= 1/2 (1-cos(4x)) ?

The answer to whether sin^2(2x)= 1/2 (1-cos(4x)) is True

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prove sin^2(2x)= 1/2 (1-cos(4x))

prove

sin^{2} (2 x) = \frac{1}{2} (1 - cos (4 x))

True

Solution steps

sin^{2} (2 x) = \frac{1}{2} (1 - cos (4 x))

Manipulating right side

\frac{1}{2} (1 - cos (4 x))

Rewrite using trig identities

= sin^{2} (2 x)

We showed that the two sides could take the same form

\Rightarrow True

sec (t) - \frac{cos ( t )}{1 + sin ( t )} = tan (t)

sec (x) - cos (x) = sin (x) \cdot tan (x)

tan (\frac{x}{2}) = \frac{tan ( x )}{sec ( x ) + 1}

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

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

Is sin^2(2x)= 1/2 (1-cos(4x)) ?
The answer to whether sin^2(2x)= 1/2 (1-cos(4x)) is True