What is the value of cos(pi/5)cos((2pi)/5) ?

The value of cos(pi/5)cos((2pi)/5) is (sqrt(2)(sqrt(5)+1)sqrt(3-\sqrt{5)})/(16)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(pi/5)cos((2pi)/5)

cos (\frac{π}{5}) cos (\frac{2 π}{5})

\frac{2 ( 5 + 1 ) 3 - 5}{16}

Solution steps

cos (\frac{π}{5}) cos (\frac{2 π}{5})

Rewrite using trig identities:

cos (\frac{2 π}{5}) = sin (\frac{π}{10})

= cos (\frac{π}{5}) sin (\frac{π}{10})

Rewrite using trig identities:

sin (\frac{π}{10}) = \frac{1 - cos ( \frac{π}{5} )}{2}

= cos (\frac{π}{5}) \frac{1 - cos ( \frac{π}{5} )}{2}

Rewrite using trig identities:

cos (\frac{π}{5}) = \frac{5 + 1}{4}

= \frac{5 + 1}{4} \frac{1 - \frac{5 + 1}{4}}{2}

Simplify

\frac{5 + 1}{4} \frac{1 - \frac{5 + 1}{4}}{2} : \frac{2 ( 5 + 1 ) 3 - 5}{16}

= \frac{2 ( 5 + 1 ) 3 - 5}{16}

arccos (- \frac{1}{3})

cos (16 0^{\circ}) cos (4 0^{\circ}) + sin (16 0^{\circ}) sin (4 0^{\circ})

0.5 sin (3 0^{\circ})

28 sin (4 5^{\circ})

arccos (\frac{8}{12})

What is the value of cos(pi/5)cos((2pi)/5) ?
The value of cos(pi/5)cos((2pi)/5) is (sqrt(2)(sqrt(5)+1)sqrt(3-\sqrt{5)})/(16)