Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Write the Value of Cos 1° + Cos 2° + Cos 3° + ... + Cos 180°. - Mathematics

Write the value of cos 1° + cos 2° + cos 3° + ... + cos 180°.

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Solution

\[\cos1^\circ + \cos2^\circ + \cos3^\circ + . . . + \cos180^\circ\]

\[ = \cos1^\circ + \cos2^\circ + \cos3^\circ + . . . + \cos88^\circ + \cos89^\circ + \cos90^\circ + \cos\left( 180 - 89 \right)^\circ + \cos\left( 180 - 88 \right)^\circ + . . . + \cos\left( 180 - 1 \right)^\circ + \cos180^\circ \left[ \cos\left( 180^\circ - \theta \right) = - \cos \theta \right]\]

\[ = \cos1^\circ + \cos2^\circ + \cos3^\circ + . . . + \cos88^\circ + \cos89^\circ + \cos90^\circ - \cos89^\circ - \cos88^\circ - . . . - \cos1^\circ + \cos180^\circ\]

\[ = \cos90^\circ + \cos180^\circ\]

\[ = 0 - 1\]

\[ = - 1\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 5 Trigonometric Functions
Q 12 | Page 41
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