What is the value of cos(45+150) ?

The value of cos(45+150) is (sqrt(2)(-sqrt(3)-1))/4

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cos(45+150)

cos (4 5^{\circ} + 15 0^{\circ})

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

Solution steps

cos (4 5^{\circ} + 15 0^{\circ})

Rewrite using trig identities:

cos (15 0^{\circ}) cos (4 5^{\circ}) - sin (15 0^{\circ}) sin (4 5^{\circ})

= cos (15 0^{\circ}) cos (4 5^{\circ}) - sin (15 0^{\circ}) sin (4 5^{\circ})

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

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

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

cos (4 5^{\circ}) + sin (4 5^{\circ})

4 cos (25 0^{\circ})

\frac{cos ( - 0.001 ) - 1}{- 0.001}

cot (2 3^{\circ})

csc (19 5^{\circ})

What is the value of cos(45+150) ?
The value of cos(45+150) is (sqrt(2)(-sqrt(3)-1))/4