- #1
smith007
- 10
- 0
Homework Statement
x in the following is actually Theta
Limit as x -> 0 (cos(x) - 1) / sin(x)
Homework Equations
none
The Attempt at a Solution
Multiply both sides by cos x +1
[ (cos x - 1) / sin x ] * [ (cos x + 1 )/ (cos x + 1)]
= [ cos2 x -1 ] / sin(x) (cos(x) +1)
= -sin2 x / sin x (cos x + 1)
- sin x / sin x cancels to -1 leaving sin x / (cos x + 1)
Sub in x -> 0
= (-1) (sin(0) / cos(0) + 1)
= (-1) (0/2) = 0
The only step I am not sure about the is cancelation of sin x /sin x. Is this allowed? How does the solution look?