Tanx/sin2x? limit x->0

2 Answers
Jun 22, 2018

lim_(x->0) tanx/sin(2x) = 1/2

Explanation:

Consider the fundamental trigonometric limit:

lim_(x->0) sinx/x =1

and note that also:

lim_(x->0) tanx/x =lim_(x->0) 1/cosx sinx/x = 1

Then:

lim_(x->0) tanx/sin(2x) = lim_(x->0) 1/2 tanx/x (2x)/sin(2x)

lim_(x->0) tanx/sin(2x) = 1/2 lim_(x->0) tanx/x lim_(x->0)(2x)/sin(2x)

lim_(x->0) tanx/sin(2x) = 1/2 *1*1 = 1/2

Jun 22, 2018

lim_(x->0) tanx/(sin2x)=1/2

Explanation:

Let L = lim_(x->0) tanx/(sin2x).

L = lim_(x->0) color(red)(sinx/cosx)/color(blue)(2sinxcosx)

L = lim_(x->0) 1/(2cos^2x)=1/(2cos^2 0)=1/2