Question

The value of `cos  π/15  cos  (2π)/15  cos  (4π)/15  cos  (8π)/15` is ______.

Options

• `1/16`

• `-1/16`

• 1

• 0

Answer 1

The value of `cos  π/15  cos  (2π)/15  cos  (4π)/15  cos  (8π)/15` is `underlinebb(-1/16)`.

Explanation:

`cos  π/15  cos  (2π)/15  cos  (4π)/15  cos  (8π)/15`

= `1/4(2 cos  (4π)/15  cos  π/15)(2 cos  (8π)/15  cos  (2π)/15)`

= `1/4(cos  π/3 + cos  π/5)(cos  (2π)/3 + cos  (2π)/5)`

= `1/4(1/2 + (sqrt(5) + 1)/4)(-1/2 + (sqrt(5) - 1)/4)`

= `1/4[-1/4 + 1/2((sqrt(5) - 1)/4 - (sqrt(5) + 1)/4) + (5 - 1)/16]`

= `-1/16`