K. C. Sinha Solutions for Chapter: Sine and Cosine Formulae and Their Applications, Exercise 1: EXERCISE 6.1

In any $∆ABC$, prove that $\left(b^2-c^2\right){\sin }^{2}A+\left(c^2-a^2\right){\sin }^{2}B+\left(a^2-b^2\right){\sin }^{2}C=0$.

If in $∆ABC, a=15,b=36,c=39$, find $\tan \frac{A}{2}$

In a $∆ABC$, if $a=18, b=24, c=30$, find $\tan \frac{A}{2},\tan \frac{B}{2},\tan \frac{C}{2}$

In a $∆ABC$, if $a=18, b=24, c=30$, find $\sin A,\sin B,\sin C$

In $∆ABC$, prove that: $\tan \frac{A}{2}\tan \frac{B}{2}\tan \frac{C}{2}=\sqrt{\left(1-\frac{a}{s}\right)\left(1-\frac{b}{s}\right)\left(1-\frac{c}{s}\right)}$

If in $∆ABC$, the difference of two angles is $60°$ and the remaining angle is $30°$, then find the ratio of the sides opposite to first two angles.

In a $∆ABC$, if $a=18, b=24, c=30$, find the area of $∆ABC$.

The sides of a quadrilateral are $3,4,5$ and $6 \mathrm{cm}$. The sum of a pair of opposite angles is $120°$. Show that the area of the quadrilateral is $3\sqrt{30} \mathrm{sq}. \mathrm{cm}$.