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)

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