The number of solutions of the pair of equations `2s in^2theta-cos2theta=0` `2cos^2theta-3sintheta=0` in the interval `[0,2pi]` is

Options

A. 0
B. 1
C. 2
D. 4

Answer

C

Explanation

`2 sin theta- cos 2 theta=0`
`rArr 2 sin^(2) theta-1 +2 sin^(2) theta=0`
`rArr sin theta = pm 1/2`
`2 cos^(2) theta- 3 sin theta=0`
`rArr sin theta=1/2` or `-2`
`:. Sin theta =1/2` (common values)
`rArr theta=pi/6, (5pi)/6" "( :. theta in [0, 2pi])`