SOLUTION: Hello! I need help solving this. Perform the addition and use the fundamental identities to simplify. 2tan x/(1+sec x)+ 2+2sec x/(tan x) Thank you

Algebra ->  Trigonometry-basics -> SOLUTION: Hello! I need help solving this. Perform the addition and use the fundamental identities to simplify. 2tan x/(1+sec x)+ 2+2sec x/(tan x) Thank you      Log On


   



Question 978218: Hello!
I need help solving this.
Perform the addition and use the fundamental identities to simplify.

2tan x/(1+sec x)+ 2+2sec x/(tan x)
Thank you

Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
2tan+x%2F%281%2Bsec+x%29%2B+2%2B2sec+x%2F%28tan+x%29+
= %282sinx%2Fcosx%29%2F%281%2B1%2Fcosx%29+%2B+2+%2B+%282%2Fcosx%29%2F%28sinx%2Fcosx%29
= 2sinx%2F%28cosx%2B1%29%2B+2+%2B2%2Fsinx
= 2sinx%281-cosx%29%2Fsin%5E2%28x%29+%2B+2+%2B+2%2Fsinx (Rationalizing 1st term)
= %282sinx+-+2+sinx%2Acosx+%2B2sin%5E2%28x%29%2B2sinx%29%2Fsin%5E2%28x%29
= %282sin%5E2%28x%29%2B4sinx-2sinx%2Acosx%29%2Fsin%5E2%28x%29
= +2+%2B+2%282-cosx%29%2Fsinx