Trig2.4

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what is the value of $\frac{\tan 40+\tan 20}{\cot 45-\cot 50 \cot 70}\,$

Given Expression is $\frac{\tan 40+\tan 20}{\cot 45-\cot 50 \cot 70}\,$

$\frac{\tan 40+\tan 20}{1-\cot (90-40) \cot (90-20}\,$

$\frac{\tan 40+\tan 20}{1-\tan 40 \tan 20}\,$ This is in the form of $\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}\,$

Therefore Given Expression = $\tan (40+20)=\tan 60=\sqrt{3}\,$

Main Page:Trigonometry

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