The value of 2cosπcos9π + cos 3π + cos 5π is

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The value of 2cos π cos 9π + cos 3π + cos 5π is
13 13 13 13

1. 1/2
2. 0
3. -1/2
4. 1/8

Correct Option: B

2cos	π	cos	9π	+ cos	3π	+ cos	5π
	13		13		13		13

= cos

π

+

9π

+ cos

π

-

9π

+ cos

3π

+ cos

5π

13

13

13

13

13

13

∵ 2 cosA cosB = cos (A + B) + cos (A – B)

= cos	10π	+ cos		-	8π		+ cos	3π	+ cos	5π
	13				13			13		13

= cos	10π	+ cos	8π	+ cos	3π	+ cos	5π
	13		13		13		13

∵ cos(-θ) = cosθ

= cos

π -

3π

+ cos

π -

5π

+ cos

3π

+ cos

5π

13

13

13

13

= - cos	3π	- cos	5π	+ cos	3π	+ cos	5π
	13		13		13		13

= 0