Question

The number of solutions of the pair of equations `2s in^2theta-cos2theta=0` `2cos^2theta-3sintheta=0` in the interval `[0,2pi]` is 0 (b) 1 (c) 2 (d) 4

Answer 1

Correct Answer - c
` 2 sin ^(2) theta - cos 2 theta = 0 `
` rArr sin ^(2) theta = (1)/(4)`
Also, ` 2 cos ^(2) theta = 3sin theta `
` therefore sin theta = (1)/(2)" " [because sin theta + 2 ne 0 ]`
` rArr ` Two solutions exist in the interval `[0, 2 pi]`.