The expression 2 cos π/13 cos 9π/13 + cos 3π/13 + cos 5π/13 is equal to

1) -1

2) 0

3) 1

4) None of these

Answer: (2) 0

Solution:

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

Using the formula 2 cos A cos B = cos(A + B) + cos(A – B),

= cos(π/13 + 9π/13) + cos(9π/13 – π/13) + cos(π/13)+ cos(5π/13)

= cos(10π/13) + cos(8π/13) + cos(3π/13) + cos(5π/13)

= {cos(10π/13) + cos(3π/13)} + {cos(8π/13) + cos(5π/13)}

Using the formula cos x + cos y = 2 cos(x + y)/2 cos(x – y)/2,

= 2 cos(10π/13 + 3π/13)/2 cos(10π/13 – 3π/13)/2 + 2 cos(8π/13 + 5π/13)/2 cos(8π/13 – 5π/13)/2

= 2 cos(π/2) cos(7π/26) + 2 cos(π/2) cos(3π/26)

= 2 (0) cos(7π/26) + 2 (0) cos(3π/26)

= 0

Was this answer helpful?

 
   

0 (0)

(1)
(1)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

Ask
Question