CUET Preparation Today
If $3 \tan \theta=2 \sqrt{3} \sin \theta, 0^{\circ}<\theta<90^{\circ}$, then find the value of $2 \sin ^2 2 \theta-3 \cos ^2 3 \theta$. |
1 $\frac{3}{2}$ $\frac{1}{2}$ $-\frac{3}{2}$ |
$\frac{3}{2}$ |
3 tanθ = 2√3 sinθ cosθ = \(\frac{√3}{2}\) { we know, cos30º = \(\frac{√3}{2}\) } Now, 2sin²2θ - 3cos²3θ = 2sin²60º - 3cos²90º = 2 × \(\frac{3}{4}\) - 0 = \(\frac{3}{2}\) |
