What is the value of cos(120+45) ?

The value of cos(120+45) is (sqrt(2)(-1-sqrt(3)))/4

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cos(120+45)

cos (12 0^{\circ} + 4 5^{\circ})

\frac{2 ( - 1 - 3 )}{4}

Solution steps

cos (12 0^{\circ} + 4 5^{\circ})

Rewrite using trig identities:

cos (12 0^{\circ}) cos (4 5^{\circ}) - sin (12 0^{\circ}) sin (4 5^{\circ})

= cos (12 0^{\circ}) cos (4 5^{\circ}) - sin (12 0^{\circ}) sin (4 5^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

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

= (- \frac{1}{2}) \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2}

Simplify

(- \frac{1}{2}) \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2} : \frac{2 ( - 1 - 3 )}{4}

= \frac{2 ( - 1 - 3 )}{4}

sin (4 4^{\circ})

csc^{2} (0)

cos (3 0^{\circ} - 4 5^{\circ})

3 cos (\frac{π}{4})

sin (39 0^{\circ})

What is the value of cos(120+45) ?
The value of cos(120+45) is (sqrt(2)(-1-sqrt(3)))/4