Question

If sec 4A = cosec(A − 20°), where 4A is an acute angle, find the value of A.

Answer 1

Given that sec 4A = cosec(A − 20°), where 4A is an acute angle.

⇒ cosec(90° − 4A) = cosec(A − 20°) (∵ sec(90° − θ) = cosec θ)

⇒ 90° − 4A = A − 20°

(By comparing angles and since, 4A is an acute angle, therefore, A − 20° is also an acute angle.)

⇒ 4A + A = 90° + 20° ⇒ 5A = 110° ⇒ A = \(\frac{110^\circ}{5}\) = 22°.

Hence, if sec 4A = cosec(A − 20°), where 4A is an acute angle, then A = 22°.