Question

The expression $\frac{\sin {22}^o\cos 8^o+\cos {158}^o\cos {98}^o}{\sin {23}^o\cos 7^o+\cos {157}^o\cos {97}^o}$ when simplified reduces to

• A. $1$
• B. $-1$
• C. $2$
• D. none of these

Answer 1

The correct option is A $1$

Given expression

$\frac{\sin {22}^{\circ }\cos 8^{\circ }+\cos {158}^{\circ }\cos {98}^{\circ }}{\sin {23}^{\circ }\cos 7^{\circ }+\cos {157}^{\circ }\cos {97}^{\circ }}$

$=\frac{\sin {22}^{\circ }\cos 8^{\circ }+\cos (180-22{)}^{\circ }\cos (90+8{)}^{\circ }}{\sin {23}^{\circ }\cos 7^{\circ }+\cos (180-23{)}^{\circ }\cos (90+7{)}^{\circ }}$

$=\frac{\sin {22}^{\circ }\cos 8^{\circ }+\cos {22}^{\circ }\sin 8^{\circ }}{\sin {23}^{\circ }\cos 7^{\circ }+\cos {23}^{\circ }\cos 7^{\circ }}$

$=\frac{\sin (22+8)}{\sin (23+7)}$

$=\frac{\sin {30}^{\circ }}{\sin {30}^{\circ }}=1$