What is the value of cos(pi/6)cos(pi/4)-sin(pi/6)sin(pi/4) ?

The value of cos(pi/6)cos(pi/4)-sin(pi/6)sin(pi/4) is (sqrt(2)(sqrt(3)-1))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(pi/6)cos(pi/4)-sin(pi/6)sin(pi/4)

cos (\frac{π}{6}) cos (\frac{π}{4}) - sin (\frac{π}{6}) sin (\frac{π}{4})

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

Solution steps

cos (\frac{π}{6}) cos (\frac{π}{4}) - sin (\frac{π}{6}) sin (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

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

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

sin^{2} (36 0^{\circ})

sin (π) - sin (\frac{π}{2})

sin (\frac{14 π}{6})

sin (21. 5^{\circ})

12 sin (3 7^{\circ})

What is the value of cos(pi/6)cos(pi/4)-sin(pi/6)sin(pi/4) ?
The value of cos(pi/6)cos(pi/4)-sin(pi/6)sin(pi/4) is (sqrt(2)(sqrt(3)-1))/4