Is sin(x/3)cos(x/3)= 1/2 sin((2x)/3) ?

The answer to whether sin(x/3)cos(x/3)= 1/2 sin((2x)/3) is True

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prove sin(x/3)cos(x/3)= 1/2 sin((2x)/3)

prove

sin (\frac{x}{3}) cos (\frac{x}{3}) = \frac{1}{2} sin (\frac{2 x}{3})

True

Solution steps

sin (\frac{x}{3}) cos (\frac{x}{3}) = \frac{1}{2} sin (\frac{2 x}{3})

Let:

u = \frac{x}{3}

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

Prove

sin (u) cos (u) = \frac{1}{2} sin (2 u) :

True

Therefore

sin (\frac{x}{3}) cos (\frac{x}{3}) = \frac{1}{2} sin (\frac{2 x}{3})

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + sec ( A )}{tan ( A ) + sin ( A )} = csc (A)

sin (x) = csc (x) - cos (x) cot (x)

sin (θ) tan (θ) = sec (θ) - cos (θ)

\frac{cot ( x ) + tan ( x )}{csc ( x )} = sec (x)

cot (θ) + 1 = csc (θ) (cos (θ) + sin (θ))

Is sin(x/3)cos(x/3)= 1/2 sin((2x)/3) ?
The answer to whether sin(x/3)cos(x/3)= 1/2 sin((2x)/3) is True