Question

If tan 2A = cot (A-${18}^{\circ }$), then find the value of A.

• A. ${18}^{\circ }$
• B. ${36}^{\circ }$
• C. ${24}^{\circ }$
• D. ${27}^{\circ }$

Answer 1

The correct option is B

${36}^{\circ }$

Given, tan 2A = cot (A - ${18}^{\circ }$)

$\Rightarrow$ tan 2A = tan (90 - (A - ${18}^{\circ }$)

$\Rightarrow$ tan 2A = tan (${108}^{\circ }$ - A)

$\Rightarrow$ 2A = ${108}^{\circ }$ - A

$\Rightarrow$ 3A = ${108}^{\circ }$

$\Rightarrow$ A = ${36}^{\circ }$