Trigonometry
posted by Jason .
Given \tan \theta = \frac{4}{3}, where \frac{\pi}{2} < \theta < \pi, what is the value of \frac{1}{\sin \theta + \cos \theta}?

I will guess that you meant:
tanØ = 4/3, π/2 < Ø < π , or Ø is in quadrant II
construct the rightangled triangle, and you should recognize the 345 triangle.
guessing that you want:
1/sinØ + cosØ
in II, the sine is + , but the cosine is 
sinØ = 4/5 and cosØ = 3/5
1/sinØ + cosØ
= 1/(4/5) + (3/5)
= 5/4  3/5
= 13/20