SOLUTION: If sec(&#952;) = x/2 for 0 < &#952; < &#960;/2 ,find an expression for ln|sec(&#952;) + tan(&#952;)| in terms of x.

Algebra ->  Trigonometry-basics -> SOLUTION: If sec(&#952;) = x/2 for 0 < &#952; < &#960;/2 ,find an expression for ln|sec(&#952;) + tan(&#952;)| in terms of x.      Log On


   

Question 1020475: If sec(θ) = x/2 for 0 < θ < π/2 ,find an expression for ln|sec(θ) + tan(θ)| in terms of x.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Note first that theta is an angle with its terminal side on the 1st quadrant, and so all its trig functions are positive.
Using the identity sec%5E2%28theta%29+=+1%2Btan%5E2%28theta%29, we get
tan%5E2%28theta%29+=+%28x%5E2+-+4%29%2F4, or tan%28theta%29+=+sqrt%28x%5E2+-+4%29%2F2, where we chose the positive square root because theta is in quadrant 1.
==> .
The absolute value bars are not necessary because tangent and secant are positive in quadrant 1.