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Prove That: Cos1° Cos2° Cos3° ... Cos180° = 0 - Mathematics

Sum

Prove that:

cos1° cos2° cos3° ... cos180° = 0

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Solution

LHS \[ = \cos1^\circ \cos2^\circ \cos3^\circ . . . \cos180^\circ \]

\[ = \cos1^\circ \times \cos2^\circ \times \cos3^\circ \times . . . \times \cos90^\circ \times . . . \cos180^\circ \]

\[ = \cos1^\circ \times \cos2^\circ \times \cos3^\circ \times . . . \times 0 \times . . . \cos180^\circ \]

= 0

= RHS

Concept: Trigonometry
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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 7 Trigonometric Ratios of Complementary Angles
Exercise | Q 6.4 | Page 313
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