Question

If $\tan 2A=\cot (A-{21}^{\circ })$, where $2A$ is an acute angle, then $\angle A=$ ____

• A. ${24}^{\circ }$
• B. ${27}^{\circ }$
• C. ${35}^{\circ }$
• D. ${37}^{\circ }$

Answer 1

The correct option is D ${37}^{\circ }$

Given, $\tan 2A=\cot (A-{21}^{\circ })$

Therefore, $\cot ({90}^{\circ }-2A)=\cot (A-{21}^{\circ })$
$\Rightarrow {90}^{\circ }-2A=A-{21}^{\circ }$

$\Rightarrow {90}^{\circ }+{21}^{\circ }=2A+A$
$\Rightarrow {111}^{\circ }=3A$

$\Rightarrow A={37}^{\circ }$
So, $\angle A={37}^{\circ }$ is correct.