Question

prove that, sinx sin2x + 2 cosx cos2x = 2 cos^3 x​

Answer 1

Answer:

2(cosx+2cos

2

x−1)+2sinxcosx.(1+2cosx)−2sinx=0

or 2(2cos

2

x+cosx−1)+2sinx(2cos

2

x+cosx−1)=0

2(1+sinx)(cosx+1)(2cosx−1)=0

We have to determine values of x s.t. −π≤x≤π

1+sinx=0 ∴sinx=−1

∴x=2nπ+ 23π

∴x=− 2π ,for n=−1 ∵−π≤x<π

cosx=−1=cosπ ∴cosx=1/2=cos(π/3)

∴x=2nπ±π/3

∴x=π/3, −π/3

Hence the values of x s.t. −π≤x≤π are−π,−π/2,−π/3,π/3,π.