The number of solutions of the pair of equations `2sin^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

We have,
`2"sin"^(2) theta - "cos" 2 theta = 0 " and " 2"cos"^(2) theta -3"sin" theta = 0`
`rArr 1-"cos" 2 theta - "cos" 2theta = 0 " and " 2-2"sin"^(2) theta - 3"sin" theta = 0`
`rArr "cos" 2 theta = (1)/(2) " and " 2 "sin"^(2) theta + 3"sin" theta -2 =0`
`rArr "cos"2 theta = (1)/(2) " and " (2"sin" theta - 1)("sin" theta + 2) = 0`
`rArr "cos" 2 theta = (1)/(2) " and sin" theta = (1)/(2)`
`rArr 2 theta = (pi)/(3), (5pi)/(3), (7pi)/(3), (11pi)/(3) " and " theta = (pi)/(6), (5pi)/(6) rArr theta = (pi)/(6), (5pi)/(6)`