What is the value of (sin(570)+2cos(1170))/(cos(1980)) ?

The value of (sin(570)+2cos(1170))/(cos(1980)) is 1/2

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(sin(570)+2cos(1170))/(cos(1980))

\frac{sin ( 57 0 ^{\circ} ) + 2 cos ( 117 0 ^{\circ} )}{cos ( 198 0 ^{\circ} )}

\frac{1}{2}

Solution steps

\frac{sin ( 57 0 ^{\circ} ) + 2 cos ( 117 0 ^{\circ} )}{cos ( 198 0 ^{\circ} )}

Simplify

= - \frac{- 2 cos ( 117 0 ^{\circ} ) - sin ( 57 0 ^{\circ} )}{cos ( 198 0 ^{\circ} )}

cos (117 0^{\circ}) = cos (9 0^{\circ})

= - \frac{- 2 cos ( 9 0 ^{\circ} ) - sin ( 57 0 ^{\circ} )}{cos ( 198 0 ^{\circ} )}

sin (57 0^{\circ}) = sin (21 0^{\circ})

= - \frac{- 2 cos ( 9 0 ^{\circ} ) - sin ( 21 0 ^{\circ} )}{cos ( 198 0 ^{\circ} )}

cos (198 0^{\circ}) = cos (18 0^{\circ})

= - \frac{- 2 cos ( 9 0 ^{\circ} ) - sin ( 21 0 ^{\circ} )}{cos ( 18 0 ^{\circ} )}

Use the following trivial identity:

cos (9 0^{\circ}) = 0

Rewrite using trig identities:

sin (21 0^{\circ}) = - \frac{1}{2}

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

= - \frac{- 2 \cdot 0 - ( - \frac{1}{2} )}{- 1}

Simplify

= \frac{1}{2}

2 cos (- \frac{π}{4}) - (- \frac{π}{4})

arctan (\frac{1}{2}) + arctan (\frac{1}{5}) + arctan (\frac{1}{8})

\frac{3}{sin ( 6 0 ^{\circ} )}

arctan (4.5)

cos^{2} (0) + sin^{2} (0)

What is the value of (sin(570)+2cos(1170))/(cos(1980)) ?
The value of (sin(570)+2cos(1170))/(cos(1980)) is 1/2