How do you find the exact value of Sec(Arctan (1/2))?

1 Answer
A. S. Adikesavan
Apr 27, 2016

2/sqrt 5

Explanation:

Let a = arc tan (1/2). Then tan a = 1/2. So, sec a = 2/sqrt 5, using sec a = +-sqrt ( 1 + tan^2a)=+-sqrt ( 1+ 1/4) = +-2/sqrt 5. Here, tan a is positive. So, sec a is positive and = 2/sqrt 5

Now, sec(arc tan (1/2))=sec(arc sec(2/sqrt 5))=2/sqrt5

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