Question

Solve: $\sec {70}^{\circ }\sin {20}^{\circ }+\cos {20}^{\circ }\text{cosec}{70}^{\circ }$

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

Answer: (D)

$2$

Given:
$\sec {70}^{\circ }\sin {20}^{\circ }+\cos {20}^{\circ }\text{cosec}{70}^{\circ }$

$=\sec {70}^{\circ }\sin ({90}^{\circ }-{70}^{\circ })+\cos {20}^{\circ }\text{cosec}({90}^{\circ }-{20}^{\circ })$

$=\sec {70}^{\circ }\cos {70}^{\circ }+\cos {20}^{\circ }\sec {20}^{\circ }$ $[\because \sin ({90}^{\circ }-\theta )=\cos \theta$ and $\text{cosec}({90}^{\circ }-\theta )=\sec \theta ]$

$=1+1$ $[\because \sec \theta .\cos \theta =1]$

$=2$

So, $2$ is correct.