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

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

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

prove

(2 sin (x) cos (x))^{4} = sin^{4} (2 x)

True

Solution steps

(2 sin (x) cos (x))^{4} = sin^{4} (2 x)

Manipulating left side

(2 sin (x) cos (x))^{4}

Rewrite using trig identities

= sin^{4} (2 x)

We showed that the two sides could take the same form

\Rightarrow True

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

csc (θ) + sec (θ) = tan (θ) + 1

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

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

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

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