Question

If sec 4A = cosec (A – 10°) and 4A is acute then A = ?
(a) 20°
(b) 25°
(c) 30°
(d) 40°

Answer 1

Given: sec4A = cosec(A – 10°)

$$\begin{gathered} \sec 4A=\mathrm{cosec}\left(A-10°\right) \\ \Rightarrow \mathrm{cosec}\left(90°-4A\right)=\mathrm{cosec}\left(A-10°\right)\left(\because \sec \theta =\mathrm{cosec}\left(90°-\theta \right)\right) \\ \Rightarrow 90°-4A=A-10° \\ \Rightarrow 90°+10°=A+4A \\ \Rightarrow 5A=100° \\ \Rightarrow A=\frac{100°}{5} \\ \Rightarrow A=20° \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{a}\right). \end{gathered}$$