If alpha + beta + gamma = 2pi , then | vedclass

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

Question

(A) Given that $\alpha + \beta + \gamma = 2\pi$.Dividing by $2$,we get $\frac{\alpha}{2} + \frac{\beta}{2} + \frac{\gamma}{2} = \pi$.Taking the tangen

Vedclass · Accepted Answer

$	an \frac{\alpha }{2} + 	an \frac{\beta }{2} + 	an \frac{\gamma }{2} = 	an \frac{\alpha }{2}	an \frac{\beta }{2}	an \frac{\gamma }{2}$

Vedclass · Answer

(A) Given that $\alpha + \beta + \gamma = 2\pi$.Dividing by $2$,we get $\frac{\alpha}{2} + \frac{\beta}{2} + \frac{\gamma}{2} = \pi$.Taking the tangent of both sides,we have $	an \left( \frac{\alpha}{2} + \frac{\beta}{2} + \frac{\gamma}{2} ight) = 	an \pi = 0$.Using the formula $	an(A+B+C) = \frac{\sum 	an A - \prod 	an A}{1 - \sum 	an A 	an B}$,we get:$\frac{	an \frac{\alpha}{2} + 	an \frac{\beta}{2} + 	an \frac{\gamma}{2} - 	an \frac{\alpha}{2} 	an \frac{\beta}{2} 	an \frac{\gamma}{2}}{1 - (	an \frac{\alpha}{2} 	an \frac{\beta}{2} + 	an \frac{\beta}{2} 	an \frac{\gamma}{2} + 	an \frac{\gamma}{2} 	an \frac{\alpha}{2})} = 0$.Since the fraction is $0$,the numerator must be $0$:$	an \frac{\alpha}{2} + 	an \frac{\beta}{2} + 	an \frac{\gamma}{2} - 	an \frac{\alpha}{2} 	an \frac{\beta}{2} 	an \frac{\gamma}{2} = 0$.Therefore,$	an \frac{\alpha}{2} + 	an \frac{\beta}{2} + 	an \frac{\gamma}{2} = 	an \frac{\alpha}{2} 	an \frac{\beta}{2} 	an \frac{\gamma}{2}$.

If $\alpha + \beta + \gamma = 2\pi ,$ then

Similar Questions

$\tan 20^\circ + \tan 40^\circ + \sqrt{3} \tan 20^\circ \tan 40^\circ = $

The value of $\cot(7.5^{\circ}) + \tan(67.5^{\circ}) - \cot(67.5^{\circ}) - \tan(7.5^{\circ})$ is:

$\frac{1}{{\sin 10^\circ }} - \frac{{\sqrt 3 }}{{\cos 10^\circ }} = $

The value of $\sin 105^{\circ} + \cos 105^{\circ}$ is

If $\frac{1+\cos A}{1-\cos A}=\frac{m^{2}}{n^{2}}$,then $\tan A=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module