SOLUTION: Write the following algebraic (non-trigonometric) expression in u, u>0. sec(cot^(-1)(sqrt(4-u^2)/u))

Algebra ->  Trigonometry-basics -> SOLUTION: Write the following algebraic (non-trigonometric) expression in u, u>0. sec(cot^(-1)(sqrt(4-u^2)/u))      Log On


   

Question 769295: Write the following algebraic (non-trigonometric) expression in u, u>0.
sec(cot^(-1)(sqrt(4-u^2)/u))
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Write the following algebraic (non-trigonometric) expression in u, u>0.
sec(cot^(-1)(sqrt(4-u^2)/u))
let x=angle of cot inverse
cotx=√((4-u^2)/u)
tanx=√(u/(4-u^2))=√(sec^2x-1)
u/(4-u^2)=sec^2x-1
sec^2x=(u/(4-u^2))+1
secx=√(u/(4-u^2)+1)
sec(cot^(-1)(sqrt(4-u^2)/u))=√(u/(4-u^2)+1)