Statement-1: The number of solutions of the simultaneous system of equations
`2"sin"^(2)theta-"cos" 2 theta =0`
`2"cos"^(2)theta - 3"sin" theta = 0" in the interval "[0, 2pi]` is two.
Statement-2: If `2"cos"^(2)theta-3"sin" theta = 0, "then" theta` does not lie in in III or IV quadrant.

Options

A. Statement -1 is true, Statement-2 is true, Statement -2 is a correct explanation for Statement-1.
B. Statement -1 is True, Statement-2 is True, Statement -2 is not a correct explanation for Statement -1.
C. Statement-1 is True, Statement-2 is False.
D. Statement -1 is False, Statement-2 is True.

Answer

A

Explanation

If `theta` lies in III or IV quadrant, then `"sin" theta lt 0`
`therefore 2 "cos"^(2) theta- 3"sin" theta gt 0`.
So, statement-2 is correct.
Now, `2"sin"^(2) theta - "cos" 2 theta = 0`
`rArr 4"sin"^(2) theta = 1 rArr "sin" theta = 1//2 " "["Using statement-2"]`
`rArr theta = (pi)/(6) "or" (5pi)/(6)`
So, statement-1 is also true.