Question

The number of values of x ∈ [0, 2π] satisfying the equation 2 sin²x = 4 + 3 cos x is______________.

Answer 1

For x ∈ [0, 2$\mathrm{\pi }$]
2sin²x = 4 + 3cos x
i.e 2(1 − cos²x) = 4 + 3cos x
i.e 2 − 2cos²x = 4 + 3cos x
⇒ 2cos²x + 3cos x + 2 = 0
⇒ 2cos²x + 4cos x − cos x + 2 = 0
i.e No solution is possible
∴ No value of x satisfies
2sin²x = 4 + 3cos x