If `sin3theta = sintheta`, how many solutions exist such that `-2piltthetalt2pi`

Options

A. 8
B. 9
C. 5
D. 7

Answer

C

Explanation

Given, `sin 3 theta-sin theta=0`
`rArr 2 cos((3theta+theta)/(2))sin((3theta-theta)/(2))=0`
`rArr cos 2 theta* sin theta=0`
`rArr cos2theta =0 or sin theta=0,pi,2pi`
`rArr 2theta=(pi)/(2),(3pi)/(2),(5pi)/(2),(7pi)/(2) or theta=pi " " [because theta in (0, 2pi)]`
`rArr theta=(pi)/(4),(3pi)/(4),(5pi)/(4),(7pi)/(4) or theta=pi`
Hence, total number of solutions are 5.