Question

The expression $S =\sec 11^{\circ} \cdot \sec 19^{\circ}-2 \cot 71^{\circ}$ reduces to:

• A. $2 \cot 11^{\circ}$
• B. $\tan 19^{\circ}$
• C. $2 \tan 11^{\circ}$
• D. $\frac{1}{2} \tan 19^{\circ}$

Answer 1

Answer: (C)

$S =\frac{1}{\cos 11^{\circ} \cos 19^{\circ}}-\frac{2 \cdot \sin 19^{\circ}}{\cos 19^{\circ}}$
$=\frac{1-2 \sin 19^{\circ} \cos 11^{\circ}}{\cos 11^{\circ} \cos 19^{\circ}}$
$=\frac{1-\left(\sin 30^{\circ}-\sin 8^{\circ}\right)}{\cos 11^{\circ} \cos 19^{\circ}}$
$=\frac{2 \cos 19^{\circ} \sin 11^{\circ}}{\cos 11^{\circ} \cos 19^{\circ}}=2 \tan 11^{\circ}$