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Question-20558




Question Number 20558 by khamizan833@gmail.com last updated on 28/Aug/17
Commented by ajfour last updated on 28/Aug/17
full form of cot x is cotangent x.
$${full}\:{form}\:{of}\:\mathrm{cot}\:{x}\:{is}\:{cotangent}\:{x}. \\ $$
Answered by Tinkutara last updated on 28/Aug/17
(1−cot 22°)(1−cot 23°)=1−cot 23°−  cot 22°+cot 22°cot 23°  cot 45°=((cot 22°cot 23°−1)/(cot 22°+cot 23°))=1  ⇒cot 22°cot 23°−cot 22°−cot 23°=1  ∴(1−cot 22°)(1−cot 23°)=2
$$\left(\mathrm{1}−\mathrm{cot}\:\mathrm{22}°\right)\left(\mathrm{1}−\mathrm{cot}\:\mathrm{23}°\right)=\mathrm{1}−\mathrm{cot}\:\mathrm{23}°− \\ $$$$\mathrm{cot}\:\mathrm{22}°+\mathrm{cot}\:\mathrm{22}°\mathrm{cot}\:\mathrm{23}° \\ $$$$\mathrm{cot}\:\mathrm{45}°=\frac{\mathrm{cot}\:\mathrm{22}°\mathrm{cot}\:\mathrm{23}°−\mathrm{1}}{\mathrm{cot}\:\mathrm{22}°+\mathrm{cot}\:\mathrm{23}°}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{cot}\:\mathrm{22}°\mathrm{cot}\:\mathrm{23}°−\mathrm{cot}\:\mathrm{22}°−\mathrm{cot}\:\mathrm{23}°=\mathrm{1} \\ $$$$\therefore\left(\mathrm{1}−\mathrm{cot}\:\mathrm{22}°\right)\left(\mathrm{1}−\mathrm{cot}\:\mathrm{23}°\right)=\mathrm{2} \\ $$

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