J P Mohindru and Bharat Mohindru Solutions for Chapter: Introduction to Trigonometry, Exercise 2: EXERCISE

If $\tan \left(A-B\right)=\frac{1}{\sqrt{3}}$ and $\tan \left(A+B\right)=\sqrt{3}, 0°<\left(A+B\right)<90°$ and $A>B$, find $A$ and $B$.

In the following figure, $△ABC$ is a right-angled triangle in which $\angle B=90°, \angle A=30°$ and $AC=20 \mathrm{cm}$. Find $AB$ and $BC$.

In a right triangle $ABC,$ right triangled at $C$, if $\angle B=60°$ and $AB=15 \mathrm{cm}$. Find the remaining angles and sides.

In a rectangle $ABCD, AB=20 \mathrm{cm}, \angle BAC=60°$, calculate the $BC$ and diagonals $AC$ and $BD$.

If $A$ and $B$ are acute angles such that $\tan A=\frac{1}{2}, \tan B=\frac{1}{3}$ and $\tan \left(A+B\right)=\frac{\tan A+\tan B}{1-\tan A\tan B}$, show that $A+B=45°$

If each of $\alpha , \beta$ and $\gamma$ is a positive acute angle such that $\sin \left(\alpha +\beta -\gamma \right)=\frac{1}{2}, \cos \left(\beta +\gamma -\alpha \right)=\frac{1}{2}$ and $\tan \left(\gamma +\alpha -\beta \right)=1$, find the values of $\alpha , \beta$ and $\gamma$.

A rhombus of side $20 \mathrm{cm}$ has two angles of $60°$ each. Find the length of the diagonals.

In the following figure $ABCD$ is a rectangle $DC=8 \mathrm{cm}$ and $BC=6 \mathrm{cm}$. Line segment $CM$ is drawn making an angle $30°$ with $DC,$ intersecting $AD$ with $M$. Find the length of $CM$ and $DM$.