Question

If $\cot A=\frac{12}{5}$ then the value of $(\sin A+\cos A)$ $\times cosec$ $A$ is

• A. $\frac{13}{5}$
• B. $\frac{17}{5}$
• C. $\frac{14}{5}$
• D. $\frac{3}{7}$

Answer 1

The correct option is B $\frac{17}{5}$

$cotA=\frac{12}{5}=\frac{B}{P}$

B=12 and P=5

$H^2=B^2+P^2$

$\Rightarrow H=\sqrt{B^2+p^2}$

$\Rightarrow H=\sqrt{{12}^2+5^2}$

$\Rightarrow H=\sqrt{144+25}$

$\Rightarrow H=\sqrt{169}=13$

Then $sinA=\frac{P}{H}=\frac{5}{13}$

$cosA=\frac{B}{H}=\frac{12}{13}$

$cosecA=\frac{H}{P}=\frac{13}{5}$

$\therefore (sinA+cosA)\times cosecA=(\frac{5}{13}+\frac{12}{13})\times \frac{13}{5}$

$\Rightarrow \frac{17}{13}\times \frac{13}{5}=\frac{17}{5}$