Considering the principal values of inverse t | vedclass

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

Question

(B) Let $	heta = \sin^{-1}\left(\frac{2}{\sqrt{13}}ight)$ and $\phi = \cos^{-1}\left(\frac{3}{\sqrt{10}}ight)$.Then $\sin 	heta = \frac{2}{\sqrt

Vedclass · Accepted Answer

$\frac{33}{56}$

Vedclass · Answer

(B) Let $	heta = \sin^{-1}\left(\frac{2}{\sqrt{13}}ight)$ and $\phi = \cos^{-1}\left(\frac{3}{\sqrt{10}}ight)$.Then $\sin 	heta = \frac{2}{\sqrt{13}}$, which implies $	an 	heta = \frac{2}{3}$.Then $\cos \phi = \frac{3}{\sqrt{10}}$, which implies $	an \phi = \frac{1}{3}$.We need to find $	an(2	heta - 2\phi) = \frac{	an 2	heta - 	an 2\phi}{1 + 	an 2	heta 	an 2\phi}$.Using $	an 2\alpha = \frac{2 	an \alpha}{1 - 	an^2 \alpha}$:$	an 2	heta = \frac{2(2/3)}{1 - (2/3)^2} = \frac{4/3}{1 - 4/9} = \frac{4/3}{5/9} = \frac{4}{3} 	imes \frac{9}{5} = \frac{12}{5}$.$	an 2\phi = \frac{2(1/3)}{1 - (1/3)^2} = \frac{2/3}{1 - 1/9} = \frac{2/3}{8/9} = \frac{2}{3} 	imes \frac{9}{8} = \frac{3}{4}$.Substituting these values:$	an(2	heta - 2\phi) = \frac{12/5 - 3/4}{1 + (12/5)(3/4)} = \frac{(48-15)/20}{1 + 36/20} = \frac{33/20}{56/20} = \frac{33}{56}$.

Considering the principal values of inverse trigonometric functions, the value of the expression $\tan\left(2 \sin^{-1}\left(\frac{2}{\sqrt{13}}\right)-2 \cos^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)$ is equal to:

Similar Questions

If $\cot \left(\cos^{-1} x\right) = \sec \left(\tan^{-1} \left(\frac{a}{\sqrt{b^2-a^2}}\right)\right)$,where $b > a > 0$,then $x =$

The number of real roots of the equation $\sin \left[2 \cos ^{-1}\left\{\cot \left(2 \tan ^{-1} x\right)\right\}\right]=0$ that are greater than or equal to $1$ are

If $y = \tan^{-1} \left( \frac{\log(e/x^3)}{\log(ex^3)} \right) + \tan^{-1} \left( \frac{\log(e^4x^3)}{\log(e/x^{12})} \right)$, for $x \in (e^{-1/3}, e^{1/12})$, then $\frac{dy}{dx}$ is equal to...

If $a, b, c$ are positive real numbers and the value of $\theta = \tan^{-1}\sqrt{\frac{a(a+b+c)}{bc}} + \tan^{-1}\sqrt{\frac{b(a+b+c)}{ca}} + \tan^{-1}\sqrt{\frac{c(a+b+c)}{ab}}$,then $\tan \theta$ is equal to

If $\tan ^{-1} \frac{1}{5}+\frac{1}{2} \sec ^{-1} x+\tan ^{-1} \frac{1}{8}=\frac{\pi}{8}$, then $x^2=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module