if x is very small how do we say sin x=tan x?

Answer 1

sinx=sinx/cosx
sinxcosx=sinx
sinxcosx-sinx=0
sinx(cosx-1)=0

sinx=0, x=0
cosx=1, x=0 also since you said x is small

Answer 2

When x=0, sin x=0 and tan x =0 , so sin x =tan x , exactly equal in this case. When x is small, the sin x and tan x are approximately equal, each of them equal to x (in radians), actually x being the first term in the series expansion of sin x as well as tan x. For x small , the higher order terms are negligible as compared to x.

Answer 3

x=0

Answer 4

tanx = sin x / cos x. When x is very small, cos x is almost 1; so sinx = tan x is more true the more x nears 0

Answer 5

x is x only in place of sin we are changing tan

Answer 6

tan X=(sin x/cos X)
where x is small cosider zero
therefore cos x=1
tan x=sin x

Answer 7

sin x = opposite/hypotenuse
tan x = adjacent/hypotenuse

if x is very small then hypoenuse = adjacent almost

qed

Answer 8

as tanx=sinx/cosx
and when x is very small i.e. x tends to zero then the denominator cosx tends to 1.
so the numerator sinx=tanx

Answer 9

tan(x) = sin(x)/cos(x)

if x -->0, cos(x)-->1, so tan(x) --> sin(x)/1 = sin(x)

Answer 10

b cos
lim sinx=x
when x------>0
and also lim tanx=x
when x----->0
so lim sinx=tanx
when x---->0