Maharashtra Board Solutions for Chapter: Trigonometric Functions, Exercise 7: Exercise 3.2

In $∆ABC$, prove that $a^3\sin \left(B-C\right)+b^3\sin \left(C-A\right)+c^3\sin \left(A-B\right)=0$.

In $∆ABC$, if $\cot A,\cot B,\cot C$ are in $\mathrm{A}.\mathrm{P}$. then show that $a^2,{ b}^2,c^2$ are also in $\mathrm{A}.\mathrm{P}$

In $∆ABC$, if $a\cos A=b\cos B$ then prove that the triangle is right angled or an isosceles triangle.

In $∆ABC$, if $a=18, b=24,c=30$ then find the values of $\cos A$

In $∆ABC,$if $a=18, b=24$ and $c=30$, then find the values of $\tan \frac{A}{2}$

In $∆ABC$, if $a=18, b=24,c=30$ then find the values of $A\left(∆ABC\right)$

In $∆ABC$, if $a=18, b=24,c=30$ then find the values of $\sin A$

In $∆ABC$ prove that $\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}=\frac{{\left[A\left(\Delta ABC\right)\right]}^2}{abcs}$