How do you simplify #sec(arctan 2)#? Trigonometry Inverse Trigonometric Functions Basic Inverse Trigonometric Functions 1 Answer Ratnaker Mehta Mar 17, 2018 # sqrt5#. Explanation: Let, #arc tan2=theta, theta in (-pi/2,pi/2)#. #:. tantheta=2>0 rArr theta in (0,pi/2)#. Hence, #sec(arc tan2)#, #=sectheta#, #=+sqrt(sec^2theta)......[because, theta in (0,pi/2)]#, #=+sqrt(1+tan^2theta)#, #=+sqrt(1+2^2)#. #rArr sec(arc tan2)=sqrt5#. Answer link Related questions What are the Basic Inverse Trigonometric Functions? How do you use inverse trig functions to find angles? How do you use inverse trigonometric functions to find the solutions of the equation that are in... How do you use inverse trig functions to solve equations? How do you evalute #sin^-1 (-sqrt(3)/2)#? How do you evalute #tan^-1 (-sqrt(3))#? How do you find the inverse of #f(x) = \frac{1}{x-5}# algebraically? How do you find the inverse of #f(x) = 5 sin^{-1}( frac{2}{x-3} )#? What is tan(arctan 10)? How do you find the #arcsin(sin((7pi)/6))#? See all questions in Basic Inverse Trigonometric Functions Impact of this question 9223 views around the world You can reuse this answer Creative Commons License