Question

general solution of 4sinx sin2x sin4x=sin3x

Answer 1

4Sinx  x  sin2x  x Sin4x  = Sin3x

[Here Use two Identities (Sin (A- B)) (Sin(A +B)) = Sin²A - Sin²B

and Sin3x = 3Sinx  - 4Sin³x]

4Sinx x Sin(3x-x) Sin(3x+x) = Sin3x

4Sinx (Sin²3x - Sin²x) = 3Sinx - 4Sin³x

4Sinx. Sin²3x - 4Sin³x = 3Sinx - 4Sin³x

4Sinx.Sin²3x  - 3Sinx = 0

Sinx (4Sin²3x - 3) =0

Sinx = 0                                         4Sin²3x - 3 = 0

x = nπ                                             Sin²3x = 3/4 = (√3/2)²

                                                      Sin²3x = Sin² (π/3)

                                                       3x  = mπ +/-  π/3

                                                         x = mπ/3 +/- π9

General Solution

X = nπ   &   x = mπ/3  +/- π/9

Where n & m are integers

Answer 2

Step-by-step explanation:

answer is

nπ or nπ/3±π/9