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

If $\cos \theta =\frac{p}{\sqrt{p^2+q^2}}$ then, find the value of $\tan \theta$.

In $△ABC$, if $\angle C=90°$ and $AC:BC=3:4$, then, what is the value of $\mathrm{cosec} \theta$?

If $\sec \theta +\tan \theta =2$ then, find the value of $\sec \theta -\tan \theta$.

If $\cos ec\theta -cot\theta =\frac{1}{2}$ then, what is the value of $\cos ec\theta +cot\theta$?

If $se{c}^2\theta +{\tan }^2\theta =\frac{13}{12}$ then, what is the value of $se{c}^4\theta -{\tan }^4\theta$?

If ${\cos }^2\theta -{\sin }^2\theta =\frac{1}{2}$ then, find the value of ${\cos }^4\theta -{\sin }^4\theta$.

If ${\cos }^4\theta -{\sin }^4\theta =\frac{2}{3}$ then, what is the value of $1-2{\sin }^2\theta$?

If $\sin \theta \cos \theta =\frac{1}{2}$ then, what is the value of ${\left(\sin \theta +\cos \theta \right)}^2$?