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If sec A = cosec(A - 36°) and 5A is an acute angle, show that A = 21°.

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Given: sec5 A = cosec(A - 36°)

=> cosec(90° − 5A) = cosecA − 36° ) [∵ cosec(90° − θ) = sec θ] 

=> 90° − 5A = A − 36° 

=> 6A = 90° + 36° 

=> 6A = 126° 

=> A = 21°

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