Question

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

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

Answer 1

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

From the equation $\alpha +\theta ={90}^{\circ }$,
we have $\theta ={90}^{\circ }-\alpha$
$cot\theta =cot({90}^{\circ }-\alpha )=tan\alpha$
$\therefore cot\theta =\frac{5}{2}$