What is the value of (sin(30))/(sin(15)) ?

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

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(sin(30))/(sin(15))

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

\frac{6 + 2}{2}

Solution steps

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

Use the following trivial identity:

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

Rewrite using trig identities:

sin (1 5^{\circ}) = \frac{6 - 2}{4}

= \frac{\frac{1}{2}}{\frac{6 - 2}{4}}

Simplify

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

= \frac{6 + 2}{2}

cos^{2} (\frac{π}{5})

arccos (- \frac{7}{3})

sin (1) + 2 (1) - 1

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

2 \cdot cos (\frac{π}{4})

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