1 (1+cos pi/ 8) (1+cos 3pi / 8) (1+cos 5pi / 8) (cos 7pi / 8)=1/8 - Maths - Trigonometric Functions

Question

1 (1+cos pi/ 8) (1+cos 3pi / 8) (1+cos 5pi / 8) (cos 7pi /
8)=1/8

Anuradha Sharma · Accepted Answer

1+cosπ81+cos3π81+cos5π81+cos7π8=1+cosπ81+cos3π81+cosπ-3π81+cosπ-π8=1+cosπ81+cos3π81-cos3π81-cosπ8As we know that cosπ-t=-cost=1+cosπ81-cosπ81+cos3π81-cos3π8=1-cos2π81-cos23π8=1-cos2π81-cosπ2-π82=1-cos2π81-sin2π8   Ascosπ2-x=sinx =sin2π8
cos2π8=14 4sin2π8
cos2π8=14sin22×π8 By double angle formula=14sin2π4=14
12=18

1.(1+cos pi/ 8) (1+cos 3pi / 8) (1+cos 5pi / 8) (cos 7pi / 8)=1/8