Question

If the value of $tan\alpha =\frac{5}{2}$ find the value of $cot\theta$ if $\alpha +\theta ={90}^{\circ }$.

• A. $\frac{5}{\sqrt{21}}$
• B. $5$
• C. $\frac{5}{2}$
• D. $\frac{\sqrt{21}}{2}$

Answer 1

The correct option is C

$\frac{5}{2}$

It is given that, $\alpha +\theta ={90}^{\circ }$,
$\Rightarrow$ $\theta ={90}^{\circ }-\alpha$
$cot\theta =cot({90}^{\circ }-\alpha )=tan\alpha$.
$\therefore cot\theta =\frac{5}{2}$.