Evaluate 75^ 15^ + 12^ 78^ - 18^ 72^ - Vidyadip

Question

Evaluate$\frac{\cos 75^{\circ}}{\sin 15^{\circ}}+\frac{\sin 12^{\circ}}{\cos 78^{\circ}}-\frac{\cos 18^{\circ}}{\sin 72^{\circ}}$

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Answer

$\frac{\cos 75^{\circ}}{\sin 15^{\circ}}+\frac{\sin 12^{\circ}}{\cos 78^{\circ}}-\frac{\cos 18^{\circ}}{\sin 72^{\circ}} $
$=\frac{\cos \left(90^{\circ}-15^{\circ}\right)}{\sin 15^{\circ}}+\frac{\sin \left(90^{\circ}-78^{\circ}\right)}{\cos 78^{\circ}}-\frac{\cos \left(90^{\circ}-72^{\circ}\right)}{\sin 72^{\circ}} $
$=\frac{\sin 15^{\circ}}{\sin 15^{\circ}}+\frac{\cos 78^{\circ}}{\cos 78^{\circ}}-\frac{\sin 72^{\circ}}{\sin 72^{\circ}} $
$=1+1-1=1$

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