What is the value of cos(36)-cos(72) ?

The value of cos(36)-cos(72) is (sqrt(5)+1)/4-(sqrt(2)sqrt(3-\sqrt{5)})/4

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cos(36)-cos(72)

cos (3 6^{\circ}) - cos (7 2^{\circ})

\frac{5 + 1}{4} - \frac{2 3 - 5}{4}

Solution steps

cos (3 6^{\circ}) - cos (7 2^{\circ})

Rewrite using trig identities:

cos (7 2^{\circ}) = sin (1 8^{\circ})

= cos (3 6^{\circ}) - sin (1 8^{\circ})

Rewrite using trig identities:

sin (1 8^{\circ}) = \frac{1 - cos ( 3 6 ^{\circ} )}{2}

= cos (3 6^{\circ}) - \frac{1 - cos ( 3 6 ^{\circ} )}{2}

Rewrite using trig identities:

cos (3 6^{\circ}) = \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{5 + 1}{4} - \frac{2 3 - 5}{4}

= \frac{5 + 1}{4} - \frac{2 3 - 5}{4}

\frac{3500 sin ( 2 )}{sin ( 5 8 ^{\circ} )}

17 cos (3 0^{\circ})

sin (3 9^{\circ}) + sin (2 1^{\circ})

\frac{sin ( π )}{tan ( π )}

3 sin (4 5^{\circ}) - 4 tan (\frac{π}{6})

What is the value of cos(36)-cos(72) ?
The value of cos(36)-cos(72) is (sqrt(5)+1)/4-(sqrt(2)sqrt(3-\sqrt{5)})/4