What is the value of tan(150)sin(315) ?

The value of tan(150)sin(315) is (sqrt(6))/6

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tan(150)sin(315)

tan (15 0^{\circ}) sin (31 5^{\circ})

\frac{6}{6}

Solution steps

tan (15 0^{\circ}) sin (31 5^{\circ})

Rewrite using trig identities:

tan (15 0^{\circ}) = - \frac{3}{3}

Rewrite using trig identities:

sin (31 5^{\circ}) = - \frac{2}{2}

= (- \frac{3}{3}) (- \frac{2}{2})

Simplify

(- \frac{3}{3}) (- \frac{2}{2}) : \frac{6}{6}

= \frac{6}{6}

sin (6 0^{\circ}) \cdot cos (3 0^{\circ}) + cos (6 0^{\circ}) \cdot sin (3 0^{\circ})

\frac{90}{sin ( 4 5 ^{\circ} )}

tan^{2} (\frac{π}{4}) + sin^{2} (\frac{π}{6}) + cos^{2} (\frac{π}{6})

cos (arccos (\frac{15}{17}) - arccos (\frac{7}{25}))

\frac{5 π}{6} + 2 cos (\frac{5 π}{6})

What is the value of tan(150)sin(315) ?
The value of tan(150)sin(315) is (sqrt(6))/6