Question

The number of solutions of the pair of equations 2sin²θ − cos²θ = 0 and 2cos²θ − 3sinθ = 0 in the interval [0, 2π] is

(A)  zero 

(B)  one 

(C)  two 

(D)  four

Answer 1

 Correct  option (C)  two 

The first equation is

2sin²θ - cos 2θ = 0 ...(1)

It can be written as

The second equation given is,

2cos²θ - 3sinθ = 0 ...(2)

It can be written as 

Hence, sinθ = 1/2 is a common solution.

Therefore, the number of solutions is two: