Question

What is the value of

$\frac{\sin 2^{\circ }\sin 4^{\circ }\sin 6^{\circ }.....\sin {88}^{\circ }}{\cos {88}^{\circ }\cos {86}^{\circ }\cos {84}^{\circ }.....\cos 2^{\circ }}$

(Do not use trigonometric tables)

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is B $1$

$\frac{\sin 2°\sin 4°\sin 6°......\sin 88°}{\cos 88°\cos 86°\cos 84°......\cos 2°}$

$=\frac{\sin (90°-88°)\sin (90°-86°)\sin (90°-84°)....\sin (90°-2°)}{\cos 88°\cos 86°\cos 84°......\cos 2°}$

$=\frac{\cos 88°\cos 86°\cos 84°......\cos 2°}{\cos 88°\cos 86°\cos 84°......\cos 2°}$

$=1$

Hence, the answer is $1.$