If tan ^{-1} x = frac{pi}{4} - tan ^{-1} left | vedclass

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

Question

(B) Given equation: $	an ^{-1} x = \frac{\pi}{4} - 	an ^{-1} \left( \frac{1}{3} ight)$ Since $\frac{\pi}{4} = 	an ^{-1}(1)$,we can write: $	an ^

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(B) Given equation: $	an ^{-1} x = \frac{\pi}{4} - 	an ^{-1} \left( \frac{1}{3} ight)$ Since $\frac{\pi}{4} = 	an ^{-1}(1)$,we can write: $	an ^{-1} x = 	an ^{-1}(1) - 	an ^{-1} \left( \frac{1}{3} ight)$ Using the formula $	an ^{-1} A - 	an ^{-1} B = 	an ^{-1} \left( \frac{A - B}{1 + AB} ight)$: $	an ^{-1} x = 	an ^{-1} \left( \frac{1 - \frac{1}{3}}{1 + 1 	imes \frac{1}{3}} ight)$ $	an ^{-1} x = 	an ^{-1} \left( \frac{\frac{2}{3}}{\frac{4}{3}} ight)$ $	an ^{-1} x = 	an ^{-1} \left( \frac{2}{4} ight)$ $	an ^{-1} x = 	an ^{-1} \left( \frac{1}{2} ight)$ Therefore,$x = \frac{1}{2}$.

If $\tan ^{-1} x = \frac{\pi}{4} - \tan ^{-1} \left( \frac{1}{3} \right)$,then $x$ is

Similar Questions

The value of $\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{8}\right)$ is

The value of $\cot \left( \sum\limits_{r = 1}^\infty \tan^{-1} \left( \frac{4}{4r^2 + 3} \right) \right)$ is equal to

Evaluate: $\cos^{-1}(\cos \frac{4\pi}{3}) + \sin^{-1}(\sin \frac{4\pi}{3}) = \dots$

Let $a_1=1, a_2, a_3, a_4, \ldots$ be consecutive natural numbers. Then $\tan ^{-1}\left(\frac{1}{1+ a _1 a _2}\right)+\tan ^{-1}\left(\frac{1}{1+ a _2 a _3}\right)+\ldots+\tan ^{-1}\left(\frac{1}{1+ a _{2021} a _{2022}}\right)$ is equal to

If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$,then $x^{100}+y^{100}+z^{100}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module