Prove the following identity?

Question

Prove the following identity?

I know this is a double angle question, but not sure how to prove it! If you could show me the steps, that would be great!

$sin (3 x) = 3 sin x - 4 {sin}^{3} x$ $sin(3x) = 3sinx - 4sin^3x$

3 Answers

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Answer 1 · 2018-03-14T08:52:39

Please see the steps below.

Explanation:

$sin 3 x = sin (x + 2 x)$ $sin3x=sin(x+2x)$

= $sin x cos 2 x + cos 2 x sin x$ $sinxcos2x+cos2xsinx$

= $sin x cos 2 x + cos x sin 2 x$ $sinxcos2x+cosxsin2x$

= $sin x (1 - 2 {sin}^{2} x) + cos x (2 sin x cos x)$ $sinx(1-2sin^2x)+cosx(2sinxcosx)$

= $sin x - 2 {sin}^{3} x + 2 sin x {cos}^{2} x$ $sinx-2sin^3x+2sinxcos^2x$

= $sin x - 2 {sin}^{3} x + 2 sin x (1 - {sin}^{2} x)$ $sinx-2sin^3x+2sinx(1-sin^2x)$

= $sin x - 2 {sin}^{3} x + 2 sin x - 2 {sin}^{3} x$ $sinx-2sin^3x+2sinx-2sin^3x$

= $3 sin x - 4 {sin}^{3} x$ $3sinx-4sin^3x$

Answer 2 · 2018-03-14T09:18:05

See Explanation.

Explanation:

$sin (3 x)$ $sin(3x)$
$= sin (2 x + x)$ $=sin(2x+x)$
$= sin 2 x cos x + cos 2 x sin x$ $=sin2xcosx + cos2xsinx$
$= (2 sin x cos x) cos x + (1 - 2 {sin}^{2} x) sin x$ $=(2 sinxcosx)cosx + (1-2sin^2x)sinx$
$= 2 sin x ({cos}^{2} x) + sin x - 2 {sin}^{3} x$ $=2sinx(cos^2x)+sinx-2sin^3x$
$= 2 sin x (1 - {sin}^{2} x) + sin x - 2 {sin}^{3} x$ $=2sinx(1-sin^2x) + sinx - 2sin^3x$
$= 2 sin x - 2 {sin}^{3} x + sin x - 2 {sin}^{3} x$ $=2sinx-2sin^3x+sinx-2sin^3x$
$= 3 sin x - 4 {sin}^{3} x$ $=3sinx - 4sin^3x$

Hope you got it.

Answer 3 · 2018-03-14T10:31:29

Kindly go through a Proof in the Explanation.

Explanation:

$sin3x=ul(sin3x-sinx)+sinx$ ,

$=2cos((3x+x)/2)sin((3x-x)/2)+sinx$ ,

$=2cos2xsinx+sinx$ ,

$=2(1-2sin^2x)sinx+sinx$ ,

$=(2sinx-4sin^3x)+sinx$ .

$rArr sin3x=3sinx-4sin^3x$ .

Science

Math

Humanities

... and beyond

Prove the following identity?

I know this is a double angle question, but not sure how to prove it! If you could show me the steps, that would be great!

$sin (3 x) = 3 sin x - 4 {sin}^{3} x$ $sin(3x) = 3sinx - 4sin^3x$

3 Answers

Explanation:

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Prove the following identity?

I know this is a double angle question, but not sure how to prove it! If you could show me the steps, that would be great! sin(3x) = 3sinx - 4sin^3xsin(3x)=3sinx−4sin3xsin(3x) = 3sinx - 4sin^3x

3 Answers

Explanation:

Explanation:

Explanation:

Related questions

Impact of this question

I know this is a double angle question, but not sure how to prove it! If you could show me the steps, that would be great!

$sin (3 x) = 3 sin x - 4 {sin}^{3} x$ $sin(3x) = 3sinx - 4sin^3x$