Question

The expression `2 cos  π/13. cos  (9π)/13 + cos  (3π)/13 + cos  (5π)/13` is equal to ______.

पर्याय

• – 1

• 0

• 1

• None of these

Answer 1

The expression `2 cos  π/13. cos  (9π)/13 + cos  (3π)/13 + cos  (5π)/13` is equal to 0.

Explanation:

`2 cos  π/13. cos  (9π)/13 + cos  (3π)/13 + cos  (5π)/13`

= `2 cos  π/13 . cos  (9π)/13 + 2 cos  (4π)/13 cos  π/13`

= `2 cos  π/13[cos  (9π)/13 + cos  (4π)/13]`

= `2 cos  π/13[2 cos  π/2. cos  (5π)/26]` ...`[∵ cos  π/2 = 0]`

= 0