Question

The value of `cos  π/8 + cos  (3π)/8 + cos  (5π)/8 + cos  (7π)/8` is ______.

विकल्प

• 0

• – 2

• 4

• `1/sqrt(3)`

Answer 1

The value of `cos  π/8 + cos  (3π)/8 + cos  (5π)/8 + cos  (7π)/8` is 0.

Explanation:

We have, `cos  π/8 + cos  (3π)/8 + cos  (5π)/8 + cos  (7π)/8`

= `cos  π/8 + cos  (3π)/8 + cos(π - (3π)/8) + cos(π - π/8)`

= `cos  π/8 + cos  (3π)/8 - cos  (3π)/8 - cos π/8`  ...[∵ cos(π – θ) = – cos θ]

= 0