Is 2sin(2θ)(1-2sin^2(θ))=sin(4θ) ?

The answer to whether 2sin(2θ)(1-2sin^2(θ))=sin(4θ) is True

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prove 2sin(2θ)(1-2sin^2(θ))=sin(4θ)

prove

2 sin (2 θ) (1 - 2 sin^{2} (θ)) = sin (4 θ)

True

Solution steps

2 sin (2 θ) (1 - 2 sin^{2} (θ)) = sin (4 θ)

Manipulating left side

2 sin (2 θ) (1 - 2 sin^{2} (θ))

Rewrite using trig identities

= sin (4 θ)

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (x) csc^{2} (x) = cot^{2} (x)

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

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

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

sin (3 x) = sin (x) (3 - 4 sin^{2} (x))

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