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Question Number 181066 by Shrinava last updated on 21/Nov/22

$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{expression}:$$$$2\mathrm{arcctg}\left(\mathrm{tg}3\right)-3\mathrm{arctg}\left(\mathrm{ctg}2\right)$$$$\mathrm{a})2\pi -3\mathrm{b})12\mathrm{c})-6\mathrm{d})\pi -4/2\mathrm{e})3\pi /2$$

Commented by mr W last updated on 22/Nov/22

$$allanswersgivenarewrong!$$

Answered by mr W last updated on 22/Nov/22

$$2{\cot }^{-1}\left(\tan 3\right)=2(\frac{\pi }{2}-3)=\pi -6$$$$3{\tan }^{-1}\left(\cot 2\right)=3(\frac{\pi }{2}-2)=\frac{3\pi }{2}-6$$$$....=\pi -6-(\frac{3\pi }{2}-6)=-\frac{\pi }{2}✓$$

Commented by Shrinava last updated on 24/Nov/22

$$\mathrm{thank}\mathrm{you}\mathrm{dera}\mathrm{professor}$$

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