Find the value of 22^ 30'. - Vidyadip

Question

Find the value of $\tan22^{\circ}30'.$

✓

Answer

We know that, $\tan\frac{\theta}{2}=\frac{\sin\frac{\theta}{2}}{\cos\frac{\theta}{2}}=\frac{2\sin\frac{\theta}{2}.\cos\frac{\theta}{2}}{2\cos^2\frac{\theta}{2}}=\frac{\sin\theta}{1+\cos\theta}$
$\therefore\ \tan22^{\circ}30'=\frac{\sin45^{\circ}}{1+\cos45^{\circ}}=\frac{\frac{1}{\sqrt2}}{1+\frac{1}{\sqrt2}}=\frac{1}{\sqrt2+1}$

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