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If-L-lim-x-pi-4-tan-3-x-tan-x-cos-x-pi-4-then-L-4-




Question Number 132079 by liberty last updated on 11/Feb/21
If L = lim_(x→π/4) ((tan^3 x−tan x)/(cos (x+(π/4))))  then (L/4) =?
IfL=limxπ/4tan3xtanxcos(x+π4)thenL4=?
Answered by EDWIN88 last updated on 11/Feb/21
 L=lim_(x→π/4) ((tan x(tan x+1)(tan x−1))/(cos (x+(π/4))))  L= 1×2×lim_(x→π/4) (((sin x−cos x)/(cos x))).((1/(cos (x+(π/4)))))  L=−1×4×lim_(x→π/4) (((1/( (√2)))cos x−(1/( (√2)))sin x)/(cos (x+(π/4))))  L=−4 ×lim_(x→π/4) ((cos (x+(π/4)))/(cos (x+(π/4)))) = −4    then (L/4) = −1
L=limxπ/4tanx(tanx+1)(tanx1)cos(x+π4)L=1×2×limxπ/4(sinxcosxcosx).(1cos(x+π4))L=1×4×limxπ/412cosx12sinxcos(x+π4)L=4×limxπ/4cos(x+π4)cos(x+π4)=4thenL4=1

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