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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sin (6 0^{\circ})

Simplify

= \frac{3}{2}

Manipulating right 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}

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ( θ )}{1 + sin ( θ )} + tan (θ) = sec (θ)

cos (x) \cdot tan (x) = sin (x)

\frac{sin ( 2 θ )}{sin ( θ )} - \frac{cos ( 2 θ )}{cos ( θ )} = sec (θ)

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

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

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