If tan A - tan B = x and cot B - cot A = y, t | vedclass

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

Question

(D) Given: $	an A - 	an B = x$ and $\cot B - \cot A = y.$ We know that $\cot B - \cot A = \frac{1}{	an B} - \frac{1}{	an A} = \frac{	an A - 	an

Vedclass · Accepted Answer

$\frac{1}{x} + \frac{1}{y}$

Vedclass · Answer

(D) Given: $	an A - 	an B = x$ and $\cot B - \cot A = y.$ We know that $\cot B - \cot A = \frac{1}{	an B} - \frac{1}{	an A} = \frac{	an A - 	an B}{	an A 	an B} = y.$ Substituting $x = 	an A - 	an B$,we get $\frac{x}{	an A 	an B} = y$,which implies $	an A 	an B = \frac{x}{y}.$ Now,$\cot (A - B) = \frac{1}{	an (A - B)} = \frac{1 + 	an A 	an B}{	an A - 	an B}.$ Substituting the values,$\cot (A - B) = \frac{1 + \frac{x}{y}}{x} = \frac{1}{x} + \frac{x}{xy} = \frac{1}{x} + \frac{1}{y}.$

If $\tan A - \tan B = x$ and $\cot B - \cot A = y,$ then $\cot (A - B) = $

Similar Questions

If $\sin A = \frac{3}{5}$,$\tan B = \frac{1}{2}$,and $\frac{\pi}{2} < A < \pi < B < \frac{3\pi}{2}$,then the value of $8 \tan A - \sqrt{5} \sec B$ is:

If $7 \sin a = 24 \cos a$,then the value of $14 \tan a - 75 \cos a - 7 \sec a$ is equal to:

If $90^{\circ} < \alpha < 180^{\circ}$,$\sin \alpha = \frac{\sqrt{3}}{2}$ and $180^{\circ} < \beta < 270^{\circ}$,$\sin \beta = -\frac{\sqrt{3}}{2}$,then $\frac{4 \sin \alpha - 3 \tan \beta}{\tan \alpha + \sin \beta} = $

If $\cos A = m \cos B,$ then

If $\cot 3A = x,$ then the value of $x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module