Q13 of 31 Page 316

If sec 5A = cosec (A + 36°) and 5A is a positive acute angle, let us find the value of A.

Given, sec5A = cosec(A + 36°)


And 5A is positive acute angle


⇒ sec5A = cosec(A + 36°)


⇒ cosec(90° - 5A) = cosec(A + 36°)


[secθ = cosec(90 - θ)]


⇒ 90 - 5A = A + 36


⇒ 90 - 36 = 6A


⇒ 6A = 54


⇒ A = 9


Hence, the value of A is 9


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