Question

Find the value of (1 + Cos π/8)×.(1+cos3π/8)×(1+cos 5π/8 ) ×(1+cos7π/8) .

Answer 1

(1+cos(π/8))*(1+cos(3π/8))*(1+cos(5π/8))*(1+cos(7π8))

= (1+cos(π8))*(1+sin(π/2−3π/8))*(1+sin(π/2−5π/8))*(1+cos(π−π/8))

= (1+cos(π8))*(1+sin(π/8))*(1−sin(π8))(1−cos(π/8))

= (1−cos2(π/8))*(1−sin2(π8))

= sin2(π8)cos2(π8)

= 1/4×(2sin(π8)cos(π8))^2

= 1/4 *sin^2(2π8)

⇒ 1/4 ×sin^2(π/4)

= 1/4 ×(1√2)^2

= 1/8