Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 1: EXERCISE 2

If $\sec \theta =\frac{5}{3}$ then, find the value of $\cos \left(90°-\theta \right)$ and $\cot \theta$.

If $\mathrm{cosec}A=\sqrt{5}$, then find the value of $\cot \left(90°-A\right)$ and $\sin \left(90°-A\right)$.

If $\theta$ and $\alpha$ are complementary angles and $\mathrm{cosec}\left(\theta -\alpha \right)=2$, then find the value of $\mathrm{cosec}\theta$ and $\mathrm{cosec}\alpha$.

If $\alpha +\beta =90°$ and $2\left({\cos }^2\alpha -{\cos }^2\beta \right)=1$, then what is the value of $\alpha$?

If $\alpha$ and $\beta$ are complementary angles and $2\cos \left(\alpha -\beta \right)=1$ then, find the value of $\alpha$ and $\beta$.

Find the value of $\tan 15°\tan 45°\tan 60°\tan 75°$.

If $ABCD$ is a cyclic quadrilateral then the value of $\tan \frac{A}{2}\tan \frac{C}{2}+\tan \frac{B}{2}\tan \frac{D}{2}$ is

The value $\cos \theta \times cosec\left(90°-\theta \right)$ is _____