cot left{frac{2019 pi}{2}-left(operatorname{c | vedclass

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Question

(A) Let $	heta = \operatorname{cosec}^{-1} \frac{5}{3} + 	an^{-1} \frac{2}{3}$.Since $\operatorname{cosec}^{-1} \frac{5}{3} = \sin^{-1} \frac{3}{5}$

Vedclass · Accepted Answer

$\frac{17}{6}$

Vedclass · Answer

(A) Let $	heta = \operatorname{cosec}^{-1} \frac{5}{3} + 	an^{-1} \frac{2}{3}$.Since $\operatorname{cosec}^{-1} \frac{5}{3} = \sin^{-1} \frac{3}{5}$,we have $	heta = \sin^{-1} \frac{3}{5} + 	an^{-1} \frac{2}{3}$.Let $\alpha = \sin^{-1} \frac{3}{5}$,then $\sin \alpha = \frac{3}{5}$,so $	an \alpha = \frac{3}{4}$.Thus,$	heta = 	an^{-1} \frac{3}{4} + 	an^{-1} \frac{2}{3}$.Using the formula $	an^{-1} x + 	an^{-1} y = 	an^{-1} \left( \frac{x+y}{1-xy} ight)$:$	heta = 	an^{-1} \left( \frac{3/4 + 2/3}{1 - (3/4)(2/3)} ight) = 	an^{-1} \left( \frac{9/12 + 8/12}{1 - 6/12} ight) = 	an^{-1} \left( \frac{17/12}{6/12} ight) = 	an^{-1} \frac{17}{6}$.The expression is $\cot \left( \frac{2019 \pi}{2} - 	heta ight)$.Since $\frac{2019 \pi}{2} = 1009 \pi + \frac{\pi}{2}$,we have $\cot \left( 1009 \pi + \frac{\pi}{2} - 	heta ight) = \cot \left( \frac{\pi}{2} - 	heta ight) = 	an 	heta$.Since $	heta = 	an^{-1} \frac{17}{6}$,$	an 	heta = \frac{17}{6}$.

$\cot \left\{\frac{2019 \pi}{2}-\left(\operatorname{cosec}^{-1} \frac{5}{3}+\tan ^{-1} \frac{2}{3}\right)\right\}$ is equal to:

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