What is the value of 2sin(30)cos(15) ?

The value of 2sin(30)cos(15) is (sqrt(6)+sqrt(2))/4

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2sin(30)cos(15)

2 sin (3 0^{\circ}) cos (1 5^{\circ})

\frac{6 + 2}{4}

Solution steps

2 sin (3 0^{\circ}) cos (1 5^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

Rewrite using trig identities:

cos (1 5^{\circ}) = \frac{6 + 2}{4}

= 2 \cdot \frac{1}{2} \cdot \frac{6 + 2}{4}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{6 + 2}{4} : \frac{6 + 2}{4}

= \frac{6 + 2}{4}

\frac{sin ^{3} ( 0 )}{3}

sin (arctan (- \frac{12}{5}))

arcsin (\frac{21}{5})

3 sin (6 8^{\circ})

cos (12 2^{\circ})

What is the value of 2sin(30)cos(15) ?
The value of 2sin(30)cos(15) is (sqrt(6)+sqrt(2))/4