Question

If tan 2A = cot (A $-$18$°$) then find the value of A where (2A) and (A-18$°$) are acute angles.

Answer 1

$$\begin{gathered} \mathrm{Given}:\tan 2\mathrm{A}=\cot (\mathrm{A}-18°);\mathrm{A}\mathrm{and}(\mathrm{A}-18°)\mathrm{are}\mathrm{acute}\mathrm{angles} \\ \mathrm{Now},\tan 2\mathrm{A}=\cot (\mathrm{A}-18°) \\ \Rightarrow \cot (90-2\mathrm{A})=\cot (\mathrm{A}-18°)[\because \tan \mathit{}x=\cot (90-x\left)\right] \\ \Rightarrow (90-2\mathrm{A})=(\mathrm{A}-18°) \\ \Rightarrow 108°=3\mathrm{A} \\ \Rightarrow \mathrm{A}=36° \end{gathered}$$