Homework Sourseevaluate limit of 1 tanX sinX cosX as X approaches pie4 p
evaluate limit of (1 - tanX) / (sinX - cosX) as X approaches pie/4
please include all the work that needs to be done to get to the answer!
please include all the work that needs to be done to get to the answer!
Solution
We know that tan(x) = sin(x)/cos(x). Then: lim (x-->pi/4) [1 - sin(x)/cos(x)] / [sin(x) - cos(x)] = lim (x-->pi/4) [cos(x) - sin(x)] / cos(x)[sin(x) - cos(x)] = -1 * lim (x-->pi/4) [sin(x) - cos(x)] / cos(x)[sin(x) - cos(x)] = -1 * lim (x-->pi/4) 1/cos(x) = -v2/2. <== ANSWER
