Question

Limit trigonometri??

Answer 1

Verified answer

Bab Limit
Matematika SMA Kelas X

lim (1/sin x - 1/tan x)
x→0
= lim (tan x - sin x) / (sin x . tan x)
  x→0
= lim ((sin x / cos x) - sin x) / (sin x . sin x / cos x)
   x→0
= lim (sin x - sin x cos x)/cos x . (cos x/sin² x)
   x→0
= lim (sin x (1 - cos x)) / sin² x)
   x→0
= lim (1 - cos x)/sin x
   x→0
= lim   (1 - cos x)/x . (x/sin x)
  x→0
= 0 . 1
= 0
 

Answer 2

Verified answer

Limit Trigometri

lim(x->0) ( 1/sin x - 1/tanx)
lim(x->0)  (1/sin x - cosx/sin x)
lim(x->0)  (1 - cos x)/(sin x)
lim(x->0)  (2 sin² 1/2 x ) / sin x
= 2 (1/2 x)² /(x)
= 1/2 x
x  =0 --> limit = 1/2(0) = 0