What is the value of cos(135+30) ?

The value of cos(135+30) is (-sqrt(6)-sqrt(2))/4

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cos(135+30)

cos (13 5^{\circ} + 3 0^{\circ})

\frac{- 6 - 2}{4}

Solution steps

cos (13 5^{\circ} + 3 0^{\circ})

Rewrite using trig identities:

cos (13 5^{\circ}) cos (3 0^{\circ}) - sin (13 5^{\circ}) sin (3 0^{\circ})

= cos (13 5^{\circ}) cos (3 0^{\circ}) - sin (13 5^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

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

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

Simplify

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

= \frac{- 6 - 2}{4}

cos (22 0^{\circ})

arcsin (\frac{19}{27})

sin (34 0^{\circ})

- arctan (0)

sin (- \frac{7 π}{2})

What is the value of cos(135+30) ?
The value of cos(135+30) is (-sqrt(6)-sqrt(2))/4