The value of (1+cos (π/6))(1+cos (π/3))(1+cos(2π/3))(1+cos(7π/6)) is

Question

The value of (1+cos (π/6))(1+cos (π/3))(1+cos(2π/3))(1+cos(7π/6)) is (A) (3/16) (B) (3/8) (C) (3/4) (D) (1/2)

Tardigrade Admin · Accepted Answer

(1+cos(π/6))(1+cos(π/3))(1+cos(2π/3))(1+cos(7π/6)) =(1+(√3/2))(1+(1/2))(1-(1/2))(1-(√3/2)) =(1-(3/4))(1-(1/4)) =(1/4)×(3/4)=(3/16)

Q. The value of $(1 + cos \frac{π}{6}) (1 + cos \frac{π}{3}) (1 + cos \frac{2 π}{3}) (1 + cos \frac{7 π}{6})$ is