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Question
Find angle A, if sec 2A = cosec (A + 48°).
Sum
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Solution
Given:
sec 2A = cosec (A + 48°)
Formula:
sec(90° − θ) = csc(θ)
Solution:
csc(90° − 2A) = csc(A + 48°) [Using the complementary relation sec 2A = csc(90° − 2A)]
90° − 2A = A + 48° [Equating the angles of equal cosecant functions]
90° − 48° = 2A + A [Rearranging terms to group like quantities]
42° = 3A [Simplifying both sides of the equation]
3A = 42° [Reversing the equation for clarity]
\[A = \frac{42^\circ}{3}\] [Dividing both sides by 3]
A = 14° [Simplifying the division]
∴ A = 14°
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