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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

= sin (x) cos (x)

= cos (x) sin (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + tan ( x )}{1 - tan ( x )} = tan (x + \frac{π}{4})

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

sin^{2} (a) cos^{2} (a) + cos^{4} (a) = cos^{2} (a)

\frac{cot ( θ )}{cos ( θ )} = csc (θ)

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

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