M L Aggarwal Solutions for Chapter: Introduction to Trigonometry, Exercise 2: Exercise 10.2

If $\theta =30°$, verify that $\tan 2\theta =\frac{2 \tan \theta }{1-{\tan }^2 \theta }$.

If $\theta =30°$, verify the following: $\cos 3\theta =4 {\cos }^3 \theta -3 \cos \theta$.

If $\theta =30°$, verify the following: $\sin 3\theta =3 \sin \theta -4 {\sin }^3 \theta$.

If $\theta =30°$, find the ratio $2 \sin \theta : \sin 2\theta$.

If $\mathrm{A}=60°$ and $\mathrm{B}=30°$, verify that $\sin \left(\mathrm{A}+\mathrm{B}\right)=\sin \mathrm{A} \cos \mathrm{B} + \cos \mathrm{A} \sin \mathrm{B}$.

If $\mathrm{A}=60°$ and $\mathrm{B}=30°$, verify that $\cos \left(\mathrm{A}+\mathrm{B}\right)=\cos \mathrm{A} \cos \mathrm{B} - \sin \mathrm{A} \sin \mathrm{B}$.

If $\mathrm{A}=60°$ and $\mathrm{B}=30°$, verify that $\tan \left(\mathrm{A}-\mathrm{B}\right)=\frac{\tan \mathrm{A} -\tan \mathrm{B}}{1+\tan \mathrm{A} \tan \mathrm{B}}$.

If $\tan \mathrm{\alpha }=\sqrt{3}$ and $\tan \mathrm{\beta }=\frac{1}{\sqrt{3}}, 0<\mathrm{\alpha }, \mathrm{\beta }<90°$, find the value of $\cot \left(\mathrm{\alpha }+\mathrm{\beta }\right)$.