KVPY Sample Paper KVPY Stream-SX Model Paper-11

If \[0\le x<\frac{\pi }{2},\] then the number of values of x for which \[x-\sin 2x+\sin 3x=0,\]

A) 2

B) 1

C) 3

D) 4

Correct Answer: A

Solution :

\[\sin x-\sin 2x+\sin 3x=0\]

\[\Rightarrow \] \[(\sin x+\sin 3x)-\sin 2x=0\]

\[\Rightarrow \] \[2\sin x,\cos x-\sin 2x=0\]

\[\Rightarrow \] \[\sin 2x\,(2\cos x-1)=0\]

\[\Rightarrow \] \[sin2x=0\]

or \[\cos x=\frac{1}{2}\]

\[\Rightarrow \] \[x=0,\frac{\pi }{3}.\]