lim x--> π/4 cos 2x 1-tan x
Matematika
nabilahsf
Pertanyaan
lim x-->π/4 cos 2x
1-tan x
1-tan x
2 Jawaban
-
1. Jawaban Ghinashoda
lim x-->π/4 cos 2x = lim x-->π/4 cos²x - sin²x
1-tan x (cosx/cosx - sinx/cosx)
= lim x-->π/4 (cos x + sinx)(cosx - sinx)
(cosx - sinx)/cosx
= lim x-->π/4 cosx (cos x + sinx)(cosx - sinx)
(cosx - sinx)
= lim x-->π/4 cosx(cosx + sinx)
= cosπ/4(cosπ/4 + sinπ/4)
= √2/2(√2/2 + √2/2)
= √2/2(√2)
= 2/2
= 1 -
2. Jawaban Yahiko
= lim x-->π/4 cosx(cosx + sinx)
= cosπ/4(cosπ/4 + sinπ/4)
= √2/2(√2/2 + √2/2)
= √2/2(√2)
= 2/2
= 1