Question

4sinx.sin2x.sin4x=3x

Answer 1

ANSWER:-

QHM

Genius

➡️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

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