Question

If sec3A=cosec(A-30), where 3A and A-30 are acute angles, find the value of A. Hence verify that sin2A-cos2A=1.

Answer 1

Answer:

A= 30°

Explanation:

sec3A=cosec(A-30°)

cosec(90°-3A)= cosec(A-30°) [∵ secA=cosec(90°-A)]

90°-3A = A-30° (∵cosec gets cancelled on both sides)

90°+30°=A+3A

120°=4A

A= 120°÷4

A= 30°

$sin^{2} 30+cos^{2} 30=1$ (∵$sin^{2} A + cosA^{2} = 1$)