If sec 2A = cosec $(A - 42^{o})$ ,where 2A is an acute angle, find the value of A.

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Solution

Sec2A=cosec(A-42°)

or, cosec(90°-2A)=cosec(A-42°) [∵, cosec(90°-θ)=secθ]

or, 90°-2A=A-42°

or, -2A-A=-42°-90°

or, -3A=-132°

or, A= $\frac{132}{3}$

or, A=44°

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