tan ^{-1}left(frac{1}{3}right)+tan ^{-1}left( | vedclass

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(B) આપણે સૂત્ર $	an ^{-1} x + 	an ^{-1} y = 	an ^{-1} \left( \frac{x+y}{1-xy} ight)$ નો ઉપયોગ કરીશું.પ્રથમ,પદોને જૂથમાં વહેંચો:$\left( 	an ^{-1}

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$\frac{\pi}{4}$

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(B) આપણે સૂત્ર $	an ^{-1} x + 	an ^{-1} y = 	an ^{-1} \left( \frac{x+y}{1-xy} ight)$ નો ઉપયોગ કરીશું.પ્રથમ,પદોને જૂથમાં વહેંચો:$\left( 	an ^{-1} \frac{1}{3} + 	an ^{-1} \frac{1}{5} ight) + \left( 	an ^{-1} \frac{1}{7} + 	an ^{-1} \frac{1}{8} ight)$પ્રથમ જોડી માટે સૂત્ર લાગુ કરતા:$	an ^{-1} \left( \frac{\frac{1}{3} + \frac{1}{5}}{1 - \frac{1}{3} 	imes \frac{1}{5}} ight) = 	an ^{-1} \left( \frac{\frac{8}{15}}{\frac{14}{15}} ight) = 	an ^{-1} \left( \frac{8}{14} ight) = 	an ^{-1} \left( \frac{4}{7} ight)$બીજી જોડી માટે સૂત્ર લાગુ કરતા:$	an ^{-1} \left( \frac{\frac{1}{7} + \frac{1}{8}}{1 - \frac{1}{7} 	imes \frac{1}{8}} ight) = 	an ^{-1} \left( \frac{\frac{15}{56}}{\frac{55}{56}} ight) = 	an ^{-1} \left( \frac{15}{55} ight) = 	an ^{-1} \left( \frac{3}{11} ight)$હવે,પરિણામોનો સરવાળો કરતા:$	an ^{-1} \left( \frac{4}{7} ight) + 	an ^{-1} \left( \frac{3}{11} ight) = 	an ^{-1} \left( \frac{\frac{4}{7} + \frac{3}{11}}{1 - \frac{4}{7} 	imes \frac{3}{11}} ight)$$= 	an ^{-1} \left( \frac{\frac{44+21}{77}}{\frac{77-12}{77}} ight) = 	an ^{-1} \left( \frac{65}{65} ight) = 	an ^{-1} (1) = \frac{\pi}{4}$

$\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{8}\right)$ નું મૂલ્ય શોધો.

Similar Questions

જો $0 < x < \frac{1}{2}$ અને $\alpha = \sin^{-1} x + \cos^{-1} \left( \frac{x}{2} + \frac{\sqrt{3 - 3 x^2}}{2} \right)$ હોય,તો $\tan \alpha + \cot \alpha =$

જો $\cos^{-1} x + \cos^{-1} y = 2\pi$ હોય,તો $\sin^{-1} x + \sin^{-1} y$ ની કિંમત શોધો.

જો $\cos^{-1} x + \cos^{-1} y + \cos^{-1} z = \pi$ હોય,તો

$2{\tan ^{ - 1}}\left( {\frac{1}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right) = $

કિંમત શોધો: $\cos ^{-1}\left(\frac{4}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)$

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