Question

The value of `(1 + cos  π/6)(1 + cos  π/3)(1 + cos  (2π)/3)(1 + cos  (7π)/6)` is equal to ______.

विकल्प

• `3/16`

• `3/8`

• `3/4`

• `1/2`

Answer 1

The value of `(1 + cos  π/6)(1 + cos  π/3)(1 + cos  (2π)/3)(1 + cos  (7π)/6)` is equal to `underlinebb(3/16)`.

Explanation:

`(1 + cos  π/6)(1 + cos  π/3)(1 + cos  (2π)/3)(1 + cos  (7π)/6)`

= `(1 + sqrt(3)/2)(1 + 1/2)(1 - 1/2)(1 - sqrt(3)/2)`

= `(1 - 3/4)(1 - 1/4)`

= `1/4 xx 3/4`

= `3/16`