যদি 1 + $\tan$^2$\theta$ = 4 এবং $\theta$ < 90° হয়, $\theta$ =?

Explanation

60°. Use the identity 1 + $\tan$^2$\theta$ = $\sec$^2$\theta$. Here that gives $\tan$^2$\theta$ = 4 - 1 = 3, so $\tan$$\theta$ = $\sqrt{3}$ (positive, since $\theta$ < 90°). The angle whose tangent is $\sqrt{3}$ is 60°. Check: $\tan$ 45° = 1 and $\tan$ 30° = \frac{1}{$\sqrt{3}$}, both too small.