For x ∈ (0, π), the equation sin x + 2sin2x −sin3x = 3 has
Infinitely many solutions
Three solutions
One solution
No solution
The correct answer is option D) No solution

The least value of R.H.S is 3 at x = π/2 while the greatest value of L.H.S is 3 at x = π/3.
Hence, L.H.S and R.H.S are not equal at the same value of x. so, no solution
Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.