First slide

Trigonometric Identities

Question

$\cos^{2} 5 ° + \cos^{2} 10 ° + \cos^{2} 15 ° + .... + \cos^{2} 360 ° =$

Moderate

A

18
B

27
C

36
D

45

Solution

If $(A + B) = 360 ° o r (A + B) = 180 °$ then $\cos^{2} A = \cos^{2} B$ and $(A + B) = 90 °$ then $(\cos^{2} A + \cos^{2} B) = 1$
$∴ \cos^{2} 5 ° + \cos^{2} 10 ° + \cos^{2} 15 ° + .... + \cos^{2} 360 ° = 4 (8 + \frac{1}{2}) + 1 + 1 (∵ \cos^{2} 180 ° = \cos^{2} 360 ° = 1) = 36$

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