Question

sinx+sin2x+sin3x=sin2x( 1+2cosx )

Answer 1

Answer: using formula sinA+sinB=2sin(A+B/2)cos (A-B/2)

Step-by-step explanation:

  prove that sinx+sin2x+sin3x=sin2x(1+2cosx)

Taking L.H.S

sinx+sin2x+sin3x

Sin3x+sinx+sin2x

Applying the above written formula on sin3x+sinx

2sin(3x+x/2) cos(3x-x/2)+sin2x

2sin2x cosx +sin2x

Taking sin 2x common

sin2x(1+2cosx)=R.H.S

Answer 2

$sin\ x + sin\ 2x + sin\ 3x = sin\ 2x(1+2cos\ x)$

Solution:

Given that, we have to prove:

$sin\ x + sin\ 2x + sin\ 3x = sin\ 2x(1+2cos\ x)$

Take the LHS

$sin\ x + sin\ 2x + sin\ 3x$ ----------- eqn 1

Use the following formula for sin 3x + sin x

$sin\ A + sin\ B = 2sin \frac{A+B}{2} cos \frac{A-B}{2}$

Therefore,

$sin\ 3x + sin\ x = 2sin\frac{3x+x}{2} cos\frac{3x-x}{2}\\\\sin\ 3x + sin\ x = 2(sin\ 2x) (cos\ x)$

Substitute the above in eqn 1

$2(sin\ 2x)(cos\ x) + sin\ 2x\\\\Take\ sin\ 2x\ as\ common\\\\sin2x(1+2cos\ x)$

Thus,

LHS = RHS

Thus proved

Learn more about this topic

Prove that: sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x

https://brainly.in/question/1549941

Solve sin3x+sin2x-sinx=0

https://brainly.in/question/2771473