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Question Number 135795 by benjo_mathlover last updated on 16/Mar/21

$$Whatthevalueof(1-\cot 23°)(1-\cot 22°).$$

Answered by MJS_new last updated on 16/Mar/21

$$(1-\cot (\frac{45}{2}-x))(1-\cot (\frac{45}{2}+x))=2$$

Answered by liberty last updated on 16/Mar/21

$$\cot 22°=\cot (45°-23°)$$$$\cot 22°=\frac{1}{\tan (45°-23°)}=\frac{1}{\frac{1-\tan 23°}{1+\tan 23°}}$$$$\cot 22°=\frac{1+\tan 23°}{1-\tan 23°}$$$$so1-\cot 22°=1-\frac{1+\tan 23°}{1-\tan 23°}=-\frac{2\tan 23°}{1-\tan 23°}$$$$then(1-\frac{1}{\tan 23°})(-\frac{2\tan 23°}{1-\tan 23°})$$$$=\frac{\tan 23°-1}{\tan 23°}\times \frac{-2\tan 23°}{1-\tan 23°}=2$$

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