R. D. Sharma Solutions for Chapter: Trigonometric Ratios, Exercise 1: EXERCISE 10.1

The value of $\tan A$ is always less than $1$.

$\mathrm{secA}=\frac{12}{5}$ for some value of angle $\mathrm{A}$.

$\mathrm{cosA}$ is the abbreviation used for the cosecant of angle $\mathrm{A}$.

$\mathrm{cotA}$ is the product of $\cot$ and $\mathrm{A}$.

$\sin \theta =\frac{4}{3}$ for some angle $\theta$.

If $\cot \theta =\frac{3}{4}$, prove that $\sqrt{\frac{\mathrm{s}\mathrm{e}\mathrm{c}\theta -\mathrm{c}\mathrm{o}\mathrm{s}ec\theta }{\mathrm{s}\mathrm{e}\mathrm{c}\theta +\mathrm{c}\mathrm{o}\mathrm{s}ec\theta }}=\frac{1}{\sqrt{7}}$.

If $3\mathrm{c}\mathrm{o}\mathrm{s}\theta -4\mathrm{s}\mathrm{i}\mathrm{n}\theta =2\mathrm{c}\mathrm{o}\mathrm{s}\theta +\mathrm{s}\mathrm{i}\mathrm{n}\theta$, find $\mathrm{t}\mathrm{a}\mathrm{n}\theta$.

If $\angle A$ and $\angle P$ are acute angles such that $\tan A=\mathrm{t}\mathrm{a}\mathrm{n} P$, then show that $\angle A=\angle P$.