If $\cos ^{2} \theta-\sin ^{2} \theta=\frac{1}{3},$ where $0 \leq \theta \leq \frac{\pi}{2},$ then the value of $\cos ^{4} \theta-\sin ^{4} \theta$ is

The value of $\sin^{2} \theta + \sin^{2}(\theta + 60^{\circ}) + \sin^{2}(\theta - 60^{\circ}) =$

The maximum value of $(7 \cos\theta + 24 \sin\theta) \times (7 \sin\theta - 24 \cos\theta)$ for every $\theta \in R$.

If $\sec \alpha + \tan \alpha = 2,$ then the value of $\sin \alpha$ is (assume that $0 < \alpha < 90^{\circ}$).

The value of ${e^{{{\log }_{10}}\tan 1^\circ + {{\log }_{10}}\tan 2^\circ + {{\log }_{10}}\tan 3^\circ + ........... + {{\log }_{10}}\tan 89^\circ }}$ is

From an aeroplane flying vertically over a straight horizontal road,the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be $30^{\circ}$ and $60^{\circ}$. Find the height of the aeroplane above the road in miles.