Question

What is the value of
$\frac{5\sin {75}^o\sin {77}^o+2\cos {13}^o\cos {15}^o}{\cos {15}^o\sin {77}^o}-\frac{7\sin {81}^o}{\cos 9^o}$

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is B $0$

$cos{13}^{\circ }=sin{77}^{\circ }\&\cos {15}^{\circ }=sin{75}^{\circ };sin{81}^{\circ }=cos{9}^{\circ }$

$\Rightarrow \frac{5sin{75}^{\circ }sin{77}^{\circ }+2sin{77}^{\circ }sin{75}^{\circ }}{sin{75}^{\circ }sin{77}^{\circ }}-\frac{7sin{81}^{\circ }}{sin{81}^{\circ }}[\because sin\theta =cos({90}^{\circ }-\theta \left)\right]$

$\Rightarrow 7-7=0$