cot left(operatorname{cosec}^{-1} frac{5}{3}+ | vedclass

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

Question

(B) આપણે $\cot \left(\operatorname{cosec}^{-1} \frac{5}{3}+	an ^{-1} \frac{2}{3}ight)$ નું મૂલ્ય શોધવાનું છે.પ્રથમ,$\operatorname{cosec}^{-1} \frac

Vedclass · Accepted Answer

$\frac{6}{17}$

Vedclass · Answer

(B) આપણે $\cot \left(\operatorname{cosec}^{-1} \frac{5}{3}+	an ^{-1} \frac{2}{3}ight)$ નું મૂલ્ય શોધવાનું છે.પ્રથમ,$\operatorname{cosec}^{-1} \frac{5}{3}$ ને $	an^{-1}$ માં ફેરવો. $\operatorname{cosec}^{-1} x = \sin^{-1} \frac{1}{x}$ હોવાથી,$\operatorname{cosec}^{-1} \frac{5}{3} = \sin^{-1} \frac{3}{5}$ થાય.ધારો કે $\sin^{-1} \frac{3}{5} = 	heta$,તો $\sin 	heta = \frac{3}{5}$. તેથી,$	an 	heta = \frac{3}{\sqrt{5^2-3^2}} = \frac{3}{4}$. આમ,$\sin^{-1} \frac{3}{5} = 	an^{-1} \frac{3}{4}$ થાય.હવે પદાવલિ $\cot \left(	an^{-1} \frac{3}{4} + 	an^{-1} \frac{2}{3}ight)$ બને છે.સૂત્ર $	an^{-1} x + 	an^{-1} y = 	an^{-1} \left(\frac{x+y}{1-xy}ight)$ નો ઉપયોગ કરતા:$	an^{-1} \frac{3}{4} + 	an^{-1} \frac{2}{3} = 	an^{-1} \left(\frac{\frac{3}{4} + \frac{2}{3}}{1 - \frac{3}{4} 	imes \frac{2}{3}}ight) = 	an^{-1} \left(\frac{\frac{9+8}{12}}{1 - \frac{6}{12}}ight) = 	an^{-1} \left(\frac{17/12}{6/12}ight) = 	an^{-1} \frac{17}{6}$.અંતે,$\cot \left(	an^{-1} \frac{17}{6}ight) = \cot \left(\cot^{-1} \frac{6}{17}ight) = \frac{6}{17}$.

$\cot \left(\operatorname{cosec}^{-1} \frac{5}{3}+\tan ^{-1} \frac{2}{3}\right)$ નું મૂલ્ય શોધો.

Similar Questions

કિંમત શોધો: $\tan^{-1}\left(\frac{1}{4}\right) + \tan^{-1}\left(\frac{2}{9}\right) = $

$x$ ના મૂલ્યોનો ગણ શોધો જેથી $\tan ^{-1}\left(\frac{x}{x-2}\right)-\tan ^{-1}\left(\frac{x}{2 x-1}\right)=\tan ^{-1}\left(\frac{2}{3}\right)$ થાય.

જો $y = \tan^{-1} \frac{x}{1+2x^2} + \tan^{-1} \frac{x}{1+6x^2} + \tan^{-1} \frac{x}{1+12x^2}$ હોય,તો $\left(\frac{dy}{dx}\right)_{x=\frac{1}{2}} = $

જો $\tan^{-1} \left[ \frac{\sqrt{5} - 2\sqrt{6}}{1 + \sqrt{6}} \right] = \frac{\pi}{3} - \tan^{-1}(k)$ હોય, તો $\sec^{-1}(k) = \dots$

કિંમત શોધો: ${\tan ^{ - 1}}x + {\cot ^{ - 1}}(x + 1)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module