What is the value of cos(135)cos(30)-sin(135)sin(30) ?

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

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cos(135)cos(30)-sin(135)sin(30)

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

\frac{- 6 - 2}{4}

Solution steps

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}

sin^{7} (6 0^{\circ})

arctan (\frac{2}{2.5})

- 5 cos (\frac{π}{6})

arcsec (1.25)

tan (69 0^{\circ})

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