What is the value of cos((5pi)/4-(5pi)/6) ?

The value of cos((5pi)/4-(5pi)/6) is (sqrt(6)-sqrt(2))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos((5pi)/4-(5pi)/6)

cos (\frac{5 π}{4} - \frac{5 π}{6})

\frac{6 - 2}{4}

Solution steps

cos (\frac{5 π}{4} - \frac{5 π}{6})

Rewrite using trig identities:

cos (\frac{5 π}{4}) cos (\frac{5 π}{6}) + sin (\frac{5 π}{4}) sin (\frac{5 π}{6})

= cos (\frac{5 π}{4}) cos (\frac{5 π}{6}) + sin (\frac{5 π}{4}) sin (\frac{5 π}{6})

Rewrite using trig identities:

cos (\frac{5 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Rewrite using trig identities:

sin (\frac{5 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

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

Simplify

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

= \frac{6 - 2}{4}

3 cos (3 π)

sin (2 \cdot 50)

\frac{10}{sin ( 3 0 ^{\circ} )}

cos (2 π) - cos (0)

cos (\frac{7 π}{4} - \frac{7 π}{6})

What is the value of cos((5pi)/4-(5pi)/6) ?
The value of cos((5pi)/4-(5pi)/6) is (sqrt(6)-sqrt(2))/4