lim x->π/4 1 - tan x/sin x - cos x
Lim x->π/4 = 1 - tan(π/4)/sin(π/4)- cos(π/4)
= 1 - tan 45°/sin 45°- cos 45°
= 1 - 1/ 1/2√2 - 1/2√2
= 0/0 -> Bentuk Tak Tentu
Pemfaktoran.
Lim x->π/4 = 1 - tan x/sin x - cos x
= 1 - sin x/cos x/sin x - cos x
= cos x/cos x - sin x/cos x/sin x - cos x
= cos x - sin x/cos x/sin x - cos x
= cos x - sin x/cos x . 1/ sin x - cos x
= -( sin x - cos x)/cos x . 1/ sin x - cos x
= - 1/cos x
= -1/cos (π/4)
= -1/1/2√2
= -√2.
Remember.
Tan x = sin x/cos x
Cos x/ Cos x = 1
Do the best and Pray hard.
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