What is the value of (sin(840))/(cos(330)+sin(315)) ?

The value of (sin(840))/(cos(330)+sin(315)) is 3+sqrt(6)

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(sin(840))/(cos(330)+sin(315))

\frac{sin ( 84 0 ^{\circ} )}{cos ( 33 0 ^{\circ} ) + sin ( 31 5 ^{\circ} )}

3 + 6

Solution steps

\frac{sin ( 84 0 ^{\circ} )}{cos ( 33 0 ^{\circ} ) + sin ( 31 5 ^{\circ} )}

Rewrite using trig identities:

sin (84 0^{\circ}) = \frac{3}{2}

Rewrite using trig identities:

cos (33 0^{\circ}) = \frac{3}{2}

Rewrite using trig identities:

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

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

Simplify

\frac{\frac{3}{2}}{\frac{3}{2} - \frac{2}{2}} : 3 + 6

= 3 + 6

cos (arctan (3) + arcsin (\frac{1}{3}))

tan (\frac{5 π}{6} - \frac{5 π}{4})

sin (arcsec (8))

- arctan (3)

sin (\frac{π}{4} - \frac{π}{2})

What is the value of (sin(840))/(cos(330)+sin(315)) ?
The value of (sin(840))/(cos(330)+sin(315)) is 3+sqrt(6)