How do you find the exact value of sec ⁡ ( tan − 1 ⁡...

Adison Rogers

Adison Rogers

Answered

2022-11-23

How do you find the exact value of sec ( tan 1 ( 3 5 ) )?

Answer & Explanation

Neil Short

Neil Short

Expert

2022-11-24Added 17 answers

Let θ = tan 1 ( 3 5 )
then tan θ = 3 5 and
sec 2 θ = 1 + tan 2 θ = 1 + 9 25 = 34 25
As tan θ is negative, as range of tan 1 is π 2 < θ < π 2 , θ lies in Q4 and sec θ is
positive and sec θ = 34 5
and hence sec ( tan 1 ( 3 5 ) )
= sec θ
= 34 5

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