Write the value of $c o s 1^{\circ} + c o s 2^{\circ} + . . . + c o s 180^{\circ} .$

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Solution

$c o s 1^{\circ} + c o s 2^{\circ} + . . . + c o s 180^{\circ}$

$= c o s (180^{\circ} - 179^{\circ}) + c o s (180^{\circ} - 178^{\circ}) + . . . + c o s 90^{\circ} + c o s 91^{\circ} + . . . . + c o s 180^{\circ}$

$= - c o s 179^{\circ} - c o s 178^{\circ} - . . . . - c o s 91^{\circ} + c o s 90^{\circ} + c o s 90^{\circ} + . . . . + c o s 180^{\circ}$

$= c o s 90^{\circ} + c o s 180^{\circ}$

=0-1

=-1

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