The general solution of equation sin x+ sin 5 x= sin 2 x+ sin 4 x is :

Question

The general solution of equation sin x+ sin 5 x= sin 2 x+ sin 4 x is : (A) (n π/2) ; n ∈ I (B) (n π/5) ; n ∈ I (C) (n π/3) ; n ∈ I (D) (2 n π/3) ; n ∈ I

Tardigrade Admin · Accepted Answer

sin x+ sin 5 x= sin 2 x+ sin 4 x ⇒ 2 sin 3 x cos 2 x=2 sin 3 x cos x ⇒ sin 3 x=0 or cos 2 x= cos x ⇒ 3 x=n π or 2 x=2 n π ± x ⇒ x=(n π/3), 2 n π, (2 n π/3) ⇒ x=(n π/3) (It includes all three possible solutions)

Q. The general solution of equation $sin x + sin 5 x = sin 2 x + sin 4 x$ is :

$\frac{nπ}{2}; n \in I$

$\frac{nπ}{5}; n \in I$

$\frac{nπ}{3}; n \in I$

$\frac{2 nπ}{3}; n \in I$

Q. The general solution of equation sinx+sin5x=sin2x+sin4x is :

2nπ​;n∈I

5nπ​;n∈I

3nπ​;n∈I

32nπ​;n∈I

sinx+sin5x=sin2x+sin4x ⇒2sin3xcos2x=2sin3xcosx ⇒sin3x=0 or cos2x=cosx ⇒3x=nπ or 2x=2nπ±x ⇒x=3nπ​,2nπ,32nπ​ ⇒x=3nπ​ (It includes all three possible solutions)

Q. The general solution of equation $sin x + sin 5 x = sin 2 x + sin 4 x$ is :

$\frac{nπ}{2}; n \in I$

$\frac{nπ}{5}; n \in I$

$\frac{nπ}{3}; n \in I$

$\frac{2 nπ}{3}; n \in I$