SOLUTION: Simplify [(1/cosx) - tgx][(1/cosx) + tgx]

Algebra ->  Trigonometry-basics -> SOLUTION: Simplify [(1/cosx) - tgx][(1/cosx) + tgx]      Log On


   

Question 949648: Simplify [(1/cosx) - tgx][(1/cosx) + tgx]
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Simplify
%28%281%2Fcos%28x%29%29+-+tg%28x%29%29%28%281%2Fcos%28x%29%29+%2B+tg%28x%29%29......note that this is the "difference of squares"
=%281%2Fcos%28x%29%29%5E2+-+tg%5E2%28x%29
=1%2Fcos%5E2%28x%29+-+tg%5E2%28x%29 ...since tg%5E2%28x%29=sin%5E2%28x%29%2Fcos%5E2%28x%29, we have
=1%2Fcos%5E2%28x%29+-+sin%5E2%28x%29%2Fcos%5E2%28x%29
=%281-+sin%5E2%28x%29%29%2Fcos%5E2%28x%29 ...........since sin%5E2%28x%29%2Bcos%5E2%28x%29=1=>cos%5E2%28x%29=1-sin%5E2%28x%29, so we have
=cos%5E2%28x%29%2Fcos%5E2%28x%29
=1