How do you find the exact value of sec^-1(sqrt2)sec1(2)?

2 Answers
Sep 1, 2016

45degrees or pi/4π4

Explanation:

Draw a. Right angled isosceles triangle . The ratio of the sides 1:1:sqrt22
Sec is hypotenuse over adjacent

Sep 1, 2016

sec^-1 sqrt2=pi/4sec12=π4.

Explanation:

The Defn. of sec^-1sec1 is :

sec^-1 x=theta , |x|.=1 iff sec theta=x, theta in [0,pi]-{pi/2}sec1x=θ,|x|.=1secθ=x,θ[0,π]{π2}.

Knowing that, sec (pi/4)= sqrt2, pi/4 in [0,2pi]-{pi/2}, sec^-1 sqrt2=pi/4sec(π4)=2,π4[0,2π]{π2},sec12=π4.