Question

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

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

Answer 1

The correct option is B ${36}^{\circ }$

$tan2A=cot(A-{18}^{\circ })$

$\because tan\theta =cot({90}^{\circ }-\theta )$

$\therefore tan2A=cot({90}^{\circ }-2A)$

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

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

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

$\Rightarrow A=\frac{108}{3}={36}^{\circ }$