How do you simplify $4 sin x + 5 sin 6 x$ $4sinx + 5sin6x$ ?

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Answer 1 · 2018-06-17T17:36:42

$The Exp. = 2 sin x {2 + 5 cos x (3 - 16 {sin}^{2} x + 16 {sin}^{4} x)}$ $"The Exp."=2sinx{2+5cosx(3-16sin^2x+16sin^4x)}$ .

$The Expression = 4 sin x + 5 sin 6 x$ $"The Expression"=4sinx+5sin6x$ ,

$= 4 sin x + 5 (2 sin 3 x cos 3 x)$ $=4sinx+5(2color(red)(sin3x)color(blue)(cos3x))$ ,

$= 4 sin x + 10 (3 sin x - 4 {sin}^{3} x) (4 {cos}^{3} x - 3 cos x)$ $=4sinx+10color(red)((3sinx-4sin^3x))color(blue)((4cos^3x-3cosx))$ ,

$= 4 sin x + 10 {sin x (3 - 4 {sin}^{2} x)} {cos x (4 {cos}^{2} x - 3)}$ $=4sinx+10{sinx(3-4sin^2x)}{cosx(4cos^2x-3)}$ ,

$= 4 sin x + 10 sin x cos x (3 - 4 {sin}^{2} x) (4 {cos}^{2} x - 3)$ $=4sinx+10sinxcosx(3-4sin^2x)(4cos^2x-3)$ ,

$= 4 sin x + 10 sin x cos x (3 - 4 {sin}^{2} x) {4 (1 - {sin}^{2} x) - 3}$ $=4sinx+10sinxcosx(3-4sin^2x){4(1-sin^2x)-3}$ ,

$= 4 sin x + 10 sin x cos x (3 - 4 {sin}^{2} x) (1 - 4 {sin}^{2} x)$ $=4sinx+10sinxcosx(3-4sin^2x)(1-4sin^2x)$ ,

$= 4 sin x + 10 sin x cos x (3 - 16 {sin}^{2} x + 16 {sin}^{4} x)$ $=4sinx+10sinxcosx(3-16sin^2x+16sin^4x)$ .

$\Rightarrow The Exp. = 2 sin x {2 + 5 cos x (3 - 16 {sin}^{2} x + 16 {sin}^{4} x)}$ $rArr"The Exp."=2sinx{2+5cosx(3-16sin^2x+16sin^4x)}$ .

How do you simplify 4sinx + 5sin6x 4sinx+5sin6x4sinx + 5sin6x ?