Is 2sin(30)cos(30)=sin(60) ?

The answer to whether 2sin(30)cos(30)=sin(60) is True

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prove 2sin(30)cos(30)=sin(60)

prove

2 sin (3 0^{\circ}) cos (3 0^{\circ}) = sin (6 0^{\circ})

True

Solution steps

2 sin (3 0^{\circ}) cos (3 0^{\circ}) = sin (6 0^{\circ})

Manipulating left side

2 sin (3 0^{\circ}) cos (3 0^{\circ})

Simplify

2 cos (3 0^{\circ}) sin (3 0^{\circ}) : \frac{3}{2}

= \frac{3}{2}

Manipulating right side

sin (6 0^{\circ})

Simplify

= \frac{3}{2}

We showed that the two sides could take the same form

\Rightarrow True

\frac{cot ( θ ) + tan ( θ )}{cot ( θ )} = sec^{2} (θ)

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

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

sin (x) = \frac{3}{4} \cdot \frac{sin ( x )}{\frac{3}{4}}

(tan (x) + 2) = 2 + sec (x) sin (x)

Is 2sin(30)cos(30)=sin(60) ?
The answer to whether 2sin(30)cos(30)=sin(60) is True