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  4. Find the value of cos 24°+ cos 5°+ cos 175°+ cos 204°+ cos 300°

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Q. Find the value of $\cos 24^{\circ}+\cos 5^{\circ}+\cos 175^{\circ}+\cos 204^{\circ}+\cos 300^{\circ}$

Trigonometric Functions

Solution:

$\cos 24^{\circ}+\cos 5^{\circ}+\cos \left(180^{\circ}-5^{\circ}\right) +\cos \left(180^{\circ}+24^{\circ}\right)+\cos\left(360^{\circ}-60^{\circ}\right)$
$=\cos 24^{\circ}+\cos 5^{\circ}-\cos 5^{\circ}-\cos 24^{\circ}+\cos 60^{\circ}$
$=1 / 2$