What is the value of cos(187.5) ?

The value of cos(187.5) is -(sqrt(2)sqrt(4+\sqrt{6)+sqrt(2)})/4

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cos(187.5)

cos (187. 5^{\circ})

- \frac{2 4 + 6 + 2}{4}

Solution steps

cos (187. 5^{\circ})

Rewrite using trig identities:

- \frac{1 + cos ( 1 5 ^{\circ} )}{2}

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

Rewrite using trig identities:

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

= - \frac{1 + \frac{6 + 2}{4}}{2}

Simplify

- \frac{1 + \frac{6 + 2}{4}}{2} : - \frac{2 4 + 6 + 2}{4}

= - \frac{2 4 + 6 + 2}{4}

1 + cos (12 0^{\circ})

2 - 2 cosh (1)

\frac{cot ^{2} ( 3 5 ^{\circ} )}{cot ^{2} ( 2 5 ^{\circ} )}

\frac{52}{cos ( 3 7 ^{\circ} )}

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

What is the value of cos(187.5) ?
The value of cos(187.5) is -(sqrt(2)sqrt(4+\sqrt{6)+sqrt(2)})/4