SOLUTION: Hello, i have been haveing truble with this trig problem for a little while. the question is, Find the identical expression for the following, (tan^2 x + 2)/ (1+tan^2 x).

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Question 872818: Hello, i have been haveing truble with this trig problem for a little while.
the question is,
Find the identical expression for the following, (tan^2 x + 2)/ (1+tan^2 x).
I have tried simplifying it to (tan^2 x + 2)/ sec ^2 x
then spliting the problem in two, (tan^2 x/ 1/ cos ^2 x) + (2/ 1/cos ^2 x)
this gave me, sin^2 x + 2cos^2 x.
This is where i get stuck, idk how to go any further to get the right answer please help me. =(
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
(tan^2 x + 2)/(1+tan^2 x)

(tan^2 x + 1 + 1)/(tan^2 x + 1)

(tan^2 x + 1)/(tan^2 x + 1) + 1/(tan^2 x + 1)

1 + 1/(sec^2 x)

1 + cos^2 x <--- You can stop here

1 + (1 - sin^2 x)

1 + 1 - sin^2 x

2 - sin^2 x <--- or you can stop here