Question

If seс (90° − 3A) . cos 48° = 1 and 0 ≤ 3A ≤ 90°; find the value of angle A.

Answer 1

Given:

seс (90° − 3A) . cos 48° = 1 and 0 ≤ 3A ≤ 90°

Formula:

\[\sec(\theta) = \frac{1}{\cos(\theta)} \text{ and } \sec(90^\circ - \theta) = \csc(\theta)\]

Solution:

\[\sec(90^\circ - 3A) = \frac{1}{\cos 48^\circ}\]  [Transposing cos 48° to the right side]

seс (90° − 3A) = sec 48°  [Using the reciprocal identity \[\frac{1}{\cos 48^\circ} = \sec 48^\circ\]]

90° − 3A = 48°  [Equating the angles of equal secant functions]

3A = 90° − 48°  [Rearranging terms to solve for 3A]

3A = 42°  [Subtracting 48° from 90°]

\[A = \frac{42^\circ}{3}\]  [Dividing both sides by 3]

A = 14°  [Simplifying the division]

∴ A = 14°