Question

Evaluate:
$2\left(\frac{\cos 58}{\sin 32}\right)-\sqrt{3}\left(\frac{\cos 38\cos ec52}{\tan 15\tan 60\tan 75}\right)$

Answer 1

$2(\frac{\cos 58}{\sin 32})-\sqrt{3}(\frac{\cos 38cosec52}{\tan 15\tan 60\tan 75})$

$2(\frac{\sin (90-58)}{\sin 32})-\sqrt{3}(\frac{\sin (90-38)cosec52}{\tan 15\tan 60\tan 75})$ $\because \sin (90-\theta )=\cos \theta$

$2(\frac{\sin 32}{\sin 32})-\sqrt{3}(\frac{\sin 52cosec52}{\cot (90-15)\tan 60\tan 75})$ $\because \cot (90-\theta )=\tan \theta$

$2(\frac{\sin 32}{\sin 32})-\sqrt{3}(\frac{\sin 52cosec52}{\cot 75\tan 60\tan 75})$

$2-\sqrt{3}(\frac{1}{\tan 60})$ $\because \sin \theta cosec\theta =1and\cot \theta \tan \theta =1$

$2-\sqrt{3}(\frac{1}{\sqrt{3}})$ $\because \tan 60=\sqrt{3}$

$2-1=1$