lim x stands to pi /4 (tan3 - tan x) / cos (x + pi/4) - Maths - Limits and Derivatives

Question

lim x stands to pi /4 (tan3 - tan x) / cos (x + pi/4)

Rishabh Mittal · Accepted Answer

Dear Student ,
Please find below the solution to the asked query :

Assuming question islimx→π4 tan3x-tan xcos x+π4=limx→π4 tan x tan2x-1cos x cos π4-sin x sin π4      Since cosA+B=cos A cos B - sin A sin B=limx→π4 tan x tan x+1 tan x-1cos x 12-sin x 12=2 limx→π4 tan x sin xcos x+1 sin xcos x-1cos x-sin x=2  limx→π4 tan x sin x+cos x sin x - cos xcos2x cos x-sin x=-2 limx→π4 tan x sin x+cos x cos2x =-2 tan π4 sin π4+cos π4cos2π4=-2 1 12+12122=- 2 2212=-4   ANS
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