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Question Number 112844 by bemath last updated on 10/Sep/20

$$\mathrm{Find}\mathrm{general}\mathrm{solution}$$$$\left(1\right)\left(\frac{\sin \mathrm{x}}{1+\mathrm{y}}\right)\frac{\mathrm{dy}}{\mathrm{dx}}=\cos \mathrm{x}$$$$\left(2\right)\mathrm{X}={\tan }^{-1}\left(\frac{2}{11}\right)+{\cot }^{-1}\left(\frac{24}{7}\right)+{\tan }^{-1}\left(\frac{1}{3}\right)$$$$\mathrm{find}\mathrm{X}.$$

Commented by bemath last updated on 12/Sep/20

Answered by john santu last updated on 10/Sep/20

$$\left(2\right)firststep.$$$${\tan }^{-1}\left(\frac{2}{11}\right)+{\cot }^{-1}\left(\frac{24}{7}\right)={\tan }^{-1}\left(\frac{2}{11}\right)+{\tan }^{-1}\left(\frac{7}{24}\right)$$$$={\tan }^{-1}\left(\frac{\frac{2}{11}+\frac{7}{24}}{1-\frac{2}{11}.\frac{7}{24}}\right)={\tan }^{-1}\left(\frac{1}{2}\right)$$$$secondstep$$$$X={\tan }^{-1}\left(\frac{1}{2}\right)+{\tan }^{-1}\left(\frac{1}{3}\right)$$$$X={\tan }^{-1}\left(\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}.\frac{1}{3}}\right)={\tan }^{-1}\left(1\right)$$$$X=\frac{\pi }{4}.$$$$\frac{JS}{amathfarmer}$$

Answered by bemath last updated on 10/Sep/20

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