If A + B + C = 180^o,then the value of cot fr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given $A + B + C = 180^o$,we have $\frac{A}{2} + \frac{B}{2} = 90^o - \frac{C}{2}$.Taking $\cot$ on both sides: $\cot(\frac{A}{2} + \frac{B}{2}) =

Vedclass · Accepted Answer

$\cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2}$

Vedclass · Answer

(C) Given $A + B + C = 180^o$,we have $\frac{A}{2} + \frac{B}{2} = 90^o - \frac{C}{2}$.Taking $\cot$ on both sides: $\cot(\frac{A}{2} + \frac{B}{2}) = \cot(90^o - \frac{C}{2})$.Using the formula $\cot(x+y) = \frac{\cot x \cot y - 1}{\cot x + \cot y}$,we get $\frac{\cot \frac{A}{2} \cot \frac{B}{2} - 1}{\cot \frac{A}{2} + \cot \frac{B}{2}} = 	an \frac{C}{2}$.Since $	an \frac{C}{2} = \frac{1}{\cot \frac{C}{2}}$,we have $\frac{\cot \frac{A}{2} \cot \frac{B}{2} - 1}{\cot \frac{A}{2} + \cot \frac{B}{2}} = \frac{1}{\cot \frac{C}{2}}$.Cross-multiplying gives $(\cot \frac{A}{2} \cot \frac{B}{2} - 1) \cot \frac{C}{2} = \cot \frac{A}{2} + \cot \frac{B}{2}$.Expanding this,we get $\cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} - \cot \frac{C}{2} = \cot \frac{A}{2} + \cot \frac{B}{2}$.Rearranging the terms,we find $\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2} = \cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2}$.

If $A + B + C = 180^o$,then the value of $\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}$ is equal to

Similar Questions

If $a$,$b$,and $c$ are non-zero real numbers,then the minimum value of the expression $\left( \frac{(a^4 + a^2 + 1)(b^4 + 7b^2 + 1)(c^4 + 11c^2 + 1)}{a^2 b^2 c^2} \right)$ is

If $A+B+C=60^{\circ}$,then $\cos (30^{\circ}-A)+\cos (30^{\circ}-B)+\cos (30^{\circ}-C)+\sin (A+B+C) = $

If $u = \sqrt{a^2 \cos^2 \theta + b^2 \sin^2 \theta} + \sqrt{a^2 \sin^2 \theta + b^2 \cos^2 \theta}$,then what is the difference between the maximum and minimum values of $u^2$?

In a $\Delta ABC$,the value of $\sin A \cos B \cos C + \sin B \cos C \cos A + \sin C \cos A \cos B$ is

The minimum value of $27^{\cos 2x} 81^{\sin 2x}$ is.......

Vedclass Test Series

Exam Paper Generator

Online Exam Module