Question

If sec 5A = cosec (A − 30°), where 5A is an acute angle, then ∠A = ?
(a) 35°
(b) 25°
(c) 20°
(d) 27°

Answer 1

$$\begin{gathered} (c)\; 20° \\ \mathrm{W}\text{e have:} \\ \left[\sec 5\text{A=cosec}(\text{A}-{30}^0)\right] \\ =>\text{cosec}({90}^0-5\text{A})=\text{cosec}(\text{A}-{30}^0)[\because \sec \theta =\text{cosec}({90}^0-\theta )] \\ =>{90}^0-5\text{A}=\text{A}-{30}^0 \\ =>-6\text{A=}-120 \\ =>\text{A=}\frac{\sout{1}\sout{2}{\sout{0}}^{20}}{{\sout{6}}_1} \\ =>{\text{A=20}}^0 \end{gathered}$$