Question

If $tan4\theta =cot(\theta -{10}^{\circ })$, where $4\theta$ and$(\theta -{10}^{\circ })$ are acute angles then the value of $\theta$ in degrees is

• A. ${16}^{\circ }$
• B. ${20}^{\circ }$
• C. ${32}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is B ${20}^{\circ }$

Given, $tan4\theta =cot(\theta -{10}^{\circ })$

This can be written as

$cot({90}^{\circ }-4\theta )=cot(\theta -{10}^{\circ })$ -----(i)

$(\because$ $Tan\theta$ = $Cot({90}^{\circ }-\theta ))$

Hence, from (i) we have

$\Rightarrow {90}^{\circ }-4\theta =\theta -{10}^{\circ }$
$\Rightarrow 5\theta ={100}^{\circ }$
$\Rightarrow \theta ={20}^{\circ }$