H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Introduction To Trigonometry, Exercise 2: EXERCISE

Prove the following

$2\left({\cos }^2 45°+{\tan }^2 60°\right)-6\left({\sin }^2 45°-{\tan }^2 30°\right)=6$

If the value of $\cos 30°=\frac{\sqrt{3}}{k}$, then, find the value of $k$.

Given that $\cos 60°=\frac{1}{2}$.

Using the formula$,$ $\tan 2A=\frac{2 \tan A}{1-{\tan }^2 A}$, If the value of $\tan 60°=\sqrt{k}$$;$ given that $\tan 30°=\frac{1}{\sqrt{3}}.$

Find the value of $k$.

Find $A$ and $B$ in the following

If $\sin (A+B)=1 \mathrm{and} \cos (A-B)=1$.

Find $A$ and $B$ in the following

If $\sin (A-B)=\frac{1}{2}$ and $\cos (A+B)=0$

The value $x$ in the following.

If $\cos (40°+x°)=\sin 30°$.

If $\frac{x {\sin }^2 30° {\cos }^2 60°}{4 {\cos }^2 45°}=\frac{3 {\sin }^2 45°+2 {\cos }^2 30°}{{\sin }^2 90°-4 {\cos }^2 45°}.$ Find the value of $x$

If $\sin (A+B+C)=1, \tan (A-B)=\frac{1}{\sqrt{3}}$ and $\sec (A+C)=2,$ find $A, B$ and $C$ when they are acute.