Question

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

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

Answer 1

The correct option is C $\frac{5}{2}$

Given, $\alpha +\theta ={90}^{\circ }.$

So, $\theta ={90}^{\circ }-\alpha$

Taking cot on both the sides,
we get,

$cot\theta =cot({90}^{\circ }-\alpha )=tan\alpha \because \left(cot\right({90}^{\circ }-\alpha )=tan\alpha )$
$\therefore cot\theta =tan\alpha =\frac{5}{2}$.