If A + B + C = frac{pi}{2},then the value of | vedclass

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

Question

(C) Given that $A + B + C = \frac{\pi}{2}$.This implies $A + B = \frac{\pi}{2} - C$.Taking the tangent on both sides,we get $	an(A + B) = 	an(\frac{

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) Given that $A + B + C = \frac{\pi}{2}$.This implies $A + B = \frac{\pi}{2} - C$.Taking the tangent on both sides,we get $	an(A + B) = 	an(\frac{\pi}{2} - C)$.Using the identity $	an(A + B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$ and $	an(\frac{\pi}{2} - C) = \cot C = \frac{1}{	an C}$,we have:$\frac{	an A + 	an B}{1 - 	an A 	an B} = \frac{1}{	an C}$.Cross-multiplying gives:$	an C(	an A + 	an B) = 1 - 	an A 	an B$.Expanding the left side:$	an C 	an A + 	an B 	an C = 1 - 	an A 	an B$.Rearranging the terms,we get:$	an A 	an B + 	an B 	an C + 	an C 	an A = 1$.

If $A + B + C = \frac{\pi}{2}$,then the value of $\tan A \tan B + \tan B \tan C + \tan C \tan A$ is

Similar Questions

If $A + B + C = 270^o,$ then $\cos 2A + \cos 2B + \cos 2C + 4\sin A \sin B \sin C = $

If $A, B, C$ are the angles of a triangle,then $\sin 2A - \sin 2B + \sin 2C =$

If $A, B, C$ are acute positive angles such that $A + B + C = \pi$ and $\cot A \cot B \cot C = K$,then:

If $\sin \theta_1 + \sin \theta_2 + \sin \theta_3 = 3$,then $\cos \theta_1 + \cos \theta_2 + \cos \theta_3 =$

In the graph of the function $\sqrt{3} \sin x + \cos x$,the maximum distance of a point from the $x$-axis is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module