Chapter1 (Q1) Use identities to find exact value .a. \(Cos (π/12)\) b. \(Cos (-7π/12)\) c. \(Cos40°cos50°-Sin40°sin50°\)d. \(Cos 7π/9 cos 2π/9+Sin 7π/9 sin 2π/9\)

Solution

a. \( Cos (π/12) ←Cos π/3-π/4
Cos (a-b) =Cosacosb+Sinasinb
Cos (a-b)=Cos π/3 cos π/4+Sin π/3 sin π/4 =1/2×√2/2+√3/2×√2/2 \)=
b. \( Cos (-7π/12)←Cos π/4-π/3
Cos (a-b)=Cosacosb+Sinasinb
Cos (a-b)=Cos π/4 cos π/3-Sin π/4 sin π/3
←= √2/2×1/2- √2/2× √3/2 \)=
c. \(Cos40°cos50°-Sin40°sin50°=Cos (40°+50° \)) =
d. \( Cos 7π/9 cos 2π/9+Sin 7π/9 sin 2π/9 \) =
Solution
a. /( =1/2×√2/2+√3/2×√2/2= (√(2+ ) √6)/4 /)
b. = /( √2/2×1/2- √2/2× √3/2= (√(2 )-√6)/4 /)
c. /( =Cos (40°+50°)=cos90°=0 /)
d. /(Cos 7π/9 cos 2π/9+Sin 7π/9 sin 2π/9= Cos -π=-1 /)