Question

If tan 2A = cot (A − 21°), where 2A is an acute angle, then ∠A = ?
(a) 24°
(b) 27°
(c) 35°
(d) 37°

Answer 1

(d) 37°

$$\begin{gathered} \text{We have:} \\ \left[\tan 2\text{A=cot}(\text{A}-{21}^0)\right] \\ =>\cot ({90}^0-2\text{A})=\cot (\text{A}-{21}^0)[\because \tan \theta =\cot ({90}^0-\theta )] \\ =>{90}^0-2\text{A}=\text{A}-{21}^0 \\ =>-3\text{A=}-111 \\ =>\text{A=}\frac{\sout{1}\sout{1}{\sout{1}}^{37}}{{\sout{3}}_1} \\ =>{\text{A=37}}^0 \end{gathered}$$