Question

lim x tends to 0 1-cos2x/3tan²x

Answer 1

Answer:

2/3

Step-by-step explanation:

1 - cos 2X = 2 sin^2 X

(2sin^2 X)/( 3 tan^2 X) = (2 cos^2 X)/ 3

Lim X tends to 0 .

So cos^2 (0) = 1

Hence 2/3

Answer 2

Answer:

$\frac{2}{3}$

Step-by-step explanation:

$lim_{x -> 0} \: \: \frac{1 - cos \: 2x}{3 {tan}^{2}x } \\ \\ \because \: 1 - cos2x = 2 {sin}^{2}x \\ \\ so \\ \\ lim_{x -> 0} \: \: \frac{ 2{sin}^{2}x }{3 {tan}^{2}x } \\ \\ we \: know \: that \\ \\ tan \: x = \frac{sin \: x}{cos \: x} \\ \\ so \\ \\ lim_{x -> 0} \: \: \frac{ 2{sin}^{2}x }{3 ( \frac{ {sin}^{2}x }{ {cos}^{2} x} ) } \\ \\ lim_{x -> 0} \: \: \frac{2}{3} {cos}^{2}x \\ \\ as \: cos 0° = 1\\ \\ apply \: limit \\ \\ \\ lim_{x -> 0} \: \: \frac{2}{3} {cos}^{2}x = \frac{2}{3}$

Hope it helps you