What is the value of cos(120)cos(45)-sin(120)sin(45) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(120)cos(45)-sin(120)sin(45)

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

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

Solution steps

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}

4 sin (\frac{π}{4}) cos (\frac{π}{4})

500 sin (3 5^{\circ})

sec (25 5^{\circ})

arcsec (5 + 3)

- 5 sin (\frac{π}{6})

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