If tan A = 2tan B + cot B, then 2tan (A - B) | vedclass

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

Question

(C) Given that $	an A = 2	an B + \cot B.$We need to find the value of $2	an (A - B).$Using the formula $	an (A - B) = \frac{	an A - 	an B}{1 + \

Vedclass · Accepted Answer

$\cot B$

Vedclass · Answer

(C) Given that $	an A = 2	an B + \cot B.$We need to find the value of $2	an (A - B).$Using the formula $	an (A - B) = \frac{	an A - 	an B}{1 + 	an A 	an B},$$2	an (A - B) = 2 \left( \frac{	an A - 	an B}{1 + 	an A 	an B} ight).$Substitute $	an A = 2	an B + \cot B$ into the expression:$2	an (A - B) = 2 \left( \frac{(2	an B + \cot B) - 	an B}{1 + (2	an B + \cot B)	an B} ight)$$= 2 \left( \frac{	an B + \cot B}{1 + 2	an^2 B + \cot B 	an B} ight)$Since $\cot B 	an B = 1,$$= 2 \left( \frac{	an B + \cot B}{1 + 2	an^2 B + 1} ight) = 2 \left( \frac{	an B + \cot B}{2 + 2	an^2 B} ight)$$= 2 \left( \frac{	an B + \cot B}{2(1 + 	an^2 B)} ight) = \frac{	an B + \cot B}{\sec^2 B}$$= \frac{	an B}{\sec^2 B} + \frac{\cot B}{\sec^2 B} = \frac{\sin B}{\cos B} \cdot \cos^2 B + \frac{\cos B}{\sin B} \cdot \cos^2 B$$= \sin B \cos B + \frac{\cos^3 B}{\sin B} = \frac{\sin^2 B \cos B + \cos^3 B}{\sin B}$$= \frac{\cos B (\sin^2 B + \cos^2 B)}{\sin B} = \frac{\cos B (1)}{\sin B} = \cot B.$

If $\tan A = 2\tan B + \cot B,$ then $2\tan (A - B) = $

Similar Questions

$A$ telegraph post is bent at a point above the ground due to a storm. Its top just touches the ground at a distance of $10 \sqrt{3} \text{ m}$ from its foot and makes an angle of $30^{\circ}$ with the horizontal. Then,the height (in meters) of the telegraph post is:

If $m$ and $M$ are the minimum and the maximum values of $4 + \frac{1}{2} \sin^2 2x - 2 \cos^4 x$ for $x \in R$,then $M - m$ is equal to

If $7 \sin ^{2} \theta+3 \cos ^{2} \theta=4,$ then $\tan \theta=$

If $A + C = B,$ then $\tan A \tan B \tan C = $

$2\cos^2 \theta - 2\sin^2 \theta = 1$,then $\theta = \dots \dots ^\circ$

Vedclass Test Series

Exam Paper Generator

Online Exam Module