The number of solutions of the equation 4 ^ 2 x - 4 ^ 3 x + 9 - 4 x...

Given: $4\sin^{2}x - 4\cos^{3}x + 9 - 4\cos x = 0$

$⇒ 4 - 4\cos^{2}x - 4\cos^{3}x + 9 - 4\cos x = 0$

$⇒ 4\cos^{3}x + 4\cos^{2}x + 4\cos x - 13 = 0$

$⇒ 4\cos^{3}x + 4\cos^{2}x + 4\cos x = 13$

We know that, $- 1 \le \cos x \le 1$

So, the maximum value of LHS is \left(4 + 4 + 4\right) = 12$</p><p>But, RHS is$13$.

So, no solutions are possible for the given equation.