Question

The value of $\frac{\sin {70}^o}{\cos {20}^o}+\frac{\text{cosec}{20}^o}{\sec {70}^o}-2\cos {70}^o\text{cosec}{20}^o$ is :

• A. $1$
• B. $2$
• C. $0$
• D. $3$

Answer 1

Answer: (C)

$0$

The value of $\frac{\sin {70}^o}{\cos {20}^o}+\frac{cosec{20}^o}{\sec {70}^o}-2\cos {70}^{o}cosec{20}^o$ is

$=\frac{\sin {70}^o}{\cos ({90}^o-{70}^o)}+\frac{cosec{20}^o}{\sec ({90}^o-{20}^o)}-\frac{2\cos {70}^o}{\sin {20}^o}$
$=\frac{\sin {70}^o}{\sin {70}^o}+\frac{cosec{20}^o}{cosec{20}^o}-\frac{2\cos {70}^o}{\sin ({90}^o-{70}^o)}$
$[\because \cos ({90}^o-\theta )\sin \theta and\sec ({90}^o-\theta )=cosec\theta ]$
$=1+1-\frac{2\cos {70}^o}{\cos {70}^o}=2-2=0$