What is the value of (sin(150)+sin(120))/(cos(210)-cos(300)) ?

The value of (sin(150)+sin(120))/(cos(210)-cos(300)) is -1

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(sin(150)+sin(120))/(cos(210)-cos(300))

\frac{sin ( 15 0 ^{\circ} ) + sin ( 12 0 ^{\circ} )}{cos ( 21 0 ^{\circ} ) - cos ( 30 0 ^{\circ} )}

- 1

Solution steps

\frac{sin ( 15 0 ^{\circ} ) + sin ( 12 0 ^{\circ} )}{cos ( 21 0 ^{\circ} ) - cos ( 30 0 ^{\circ} )}

Rewrite using trig identities:

cos (21 0^{\circ}) - cos (30 0^{\circ}) = 2 sin (4 5^{\circ}) sin (25 5^{\circ})

= \frac{sin ( 15 0 ^{\circ} ) + sin ( 12 0 ^{\circ} )}{2 sin ( 4 5 ^{\circ} ) sin ( 25 5 ^{\circ} )}

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

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

Rewrite using trig identities:

sin (25 5^{\circ}) = \frac{- 2 - 6}{4}

= \frac{\frac{1}{2} + \frac{3}{2}}{2 \cdot \frac{2}{2} \cdot \frac{- 2 - 6}{4}}

Simplify

\frac{\frac{1}{2} + \frac{3}{2}}{2 \cdot \frac{2}{2} \cdot \frac{- 2 - 6}{4}} : - 1

= - 1

sin (\frac{π}{16})

cos (\frac{12 π}{3})

sec (- 2)

sin (2 \cdot 45)

- 4 cos (\frac{3 π}{4})

What is the value of (sin(150)+sin(120))/(cos(210)-cos(300)) ?
The value of (sin(150)+sin(120))/(cos(210)-cos(300)) is -1