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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

cos^{3} (θ) + sin^{2} (θ) cos (θ) = cos (θ)

cot^{2} (a) = cos^{2} (a) + ((cot (a)) (cos (a)))^{2}

(1 - sin^{2} (t)) (1 + tan^{2} (t)) = 1

1 - cosh^{2} (x) = - sinh^{2} (x)

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

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