What is the value of (sin(150)+sin(30))/(cos(120)+cos(240)) ?

The value of (sin(150)+sin(30))/(cos(120)+cos(240)) is -1

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(sin(150)+sin(30))/(cos(120)+cos(240))

\frac{sin ( 15 0 ^{\circ} ) + sin ( 3 0 ^{\circ} )}{cos ( 12 0 ^{\circ} ) + cos ( 24 0 ^{\circ} )}

- 1

Solution steps

\frac{sin ( 15 0 ^{\circ} ) + sin ( 3 0 ^{\circ} )}{cos ( 12 0 ^{\circ} ) + cos ( 24 0 ^{\circ} )}

Rewrite using trig identities:

cos (24 0^{\circ}) = 2 cos^{2} (12 0^{\circ}) - 1

= \frac{sin ( 15 0 ^{\circ} ) + sin ( 3 0 ^{\circ} )}{cos ( 12 0 ^{\circ} ) + 2 cos ^{2} ( 12 0 ^{\circ} ) - 1}

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

= \frac{\frac{1}{2} + \frac{1}{2}}{- \frac{1}{2} + 2 ( - \frac{1}{2} ) ^{2} - 1}

Simplify

\frac{\frac{1}{2} + \frac{1}{2}}{- \frac{1}{2} + 2 ( - \frac{1}{2} ) ^{2} - 1} : - 1

= - 1

- 6 sin (3 0^{\circ}) + 2 cos (6 0^{\circ})

arcsin (\frac{9.2}{15.6})

arccos (0.371)

arccos (sin (- \frac{11 π}{4}))

arcsech (0)

What is the value of (sin(150)+sin(30))/(cos(120)+cos(240)) ?
The value of (sin(150)+sin(30))/(cos(120)+cos(240)) is -1