Question

Find the exact value of each expression

sec 30◦ cos 30◦ − tan 60◦ cot 60◦

Answer 1

Let us find the exact value of the expression

$\sec 30^{\circ}\cdot \cos 30^{\circ} − \tan 60^{\circ} \cdot\cot 60^{\circ} =\frac{1}{\cos 30^{\circ}}\cos 30^{\circ}-\frac{\sin 60^{\circ} }{\cos 60^{\circ}}\frac{\cos 60^{\circ}}{\sin 60^{\circ}}=1-1=0.$