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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan (x) (1 - sin^{2} (x))

Express with sin, cos

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

Rewrite using trig identities

= \frac{sin ( 2 x )}{2}

Manipulating right side

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

Simplify

= \frac{sin ( 2 x )}{2}

We showed that the two sides could take the same form

\Rightarrow True

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

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

sin (x) + cos (x) \cdot cot (x) = csc (x)

cos (4 x) = 1 - 8 sin^{2} (x) cos^{2} (x)

\frac{sin ( x )}{1 - cos ( - x )} = csc (x) + cot (x)

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