Question

find the one sided limit f(x) = square root of 1-cos2x /x ,as x approaches 0

Answer 1

is it
\[\sqrt{1-\cos^2(x)}\] or
\[\sqrt{1-\cos(2x)}\]

Answer 2

it is \[\frac{ \sqrt{1- \cos 2x} }{ x }\]

Answer 3

does it help to know that
\[1-\cos(2x)=2\sin^2(x)\]?

Answer 4

it is 2x not \[x^{2}\]

Answer 5

some trig identity you forget as soon as you stop looking at trig identities

Answer 6

how does 1−cos(2x) becomes 2sin^2(x)

Answer 7

i was trying to prove that but could not .

Answer 8

the one that starts
\[\cos(2x)=1-\sin^2(x)\]

Answer 9

i guess it depends on how far back you want to go, but that is one of the "double angle" formulas for cosine

Answer 10

but can i use cos^2x + sin^2x=1 identity to derive it?

Answer 11

no

Answer 12

no it comes from angle sum identity
\[\cos(x+x) = \cos^2 x - \sin^2 x\]
then you can use pythagorean identity
cos^2 = 1-sin^2

Answer 13

unless it was
\[\sqrt{1-\cos^2(x)}\] in which case the answer is different
i thought you said it was
\[\sqrt{1-\cos(2x)}\]

Answer 14

like i said, depends on how far back you want to do

Answer 15

Thank you i have understood now.

Answer 16

yw