The number of real roots of the equation `cos e ctheta+sectheta-sqrt(15)=0` ling in `[0,pi]` is. 6 (b) 8 (c) 4 (d) 0

Options

A. 6
B. 8
C. 4
D. 0

Answer

C

Explanation

The given equation becomes
`sin theta + cos theta =sqrt(15) sin theta cos theta`
Squaring, `1 + sin 2 theta = 15 sin^(2) theta cos^(2) theta`
`1+sin 2 theta =15/4 sin^(2) 2 theta`
`rArr 15 sin^(2) 2 theta-4 sin 2 theta-4=0`
`rArr sin 2 theta=2/3, -2/5`
As `theta` varies from 0 to `pi, 2 theta` varies from 0 to `2pi`.
corresponding to `sin 2 theta=2/3`, there are two solutions.