If sec 4A = cosec (A – 10°) and 4A is acute then A = ?


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



Given: sec4A = cosec(– 10°)

$\sec 4 A=\operatorname{cosec}\left(A-10^{\circ}\right)$

$\Rightarrow \operatorname{cosec}\left(90^{\circ}-4 A\right)=\operatorname{cosec}\left(A-10^{\circ}\right) \quad\left(\because \sec \theta=\operatorname{cosec}\left(90^{\circ}-\theta\right)\right)$

$\Rightarrow 90^{\circ}-4 A=A-10^{\circ}$

$\Rightarrow 90^{\circ}+10^{\circ}=A+4 A$

$\Rightarrow 5 A=100^{\circ}$

$\Rightarrow A=\frac{100^{\circ}}{5}$

$\Rightarrow A=20^{\circ}$

Hence, the correct option is (a).


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