Help proving that Ln(tanx)=Ln(sinx)-sin(cosx)??

Question

I know that Ln means natural log but what how do you prove it? I dont know where to start lol

ln(tanx)=ln(sinx)-sin(cosx)

Answer 1

ln[tan x] = ln[sin x/cos x] = ln[sin x] - ln[cos x]

Answer 2

You wrote it wrong
ln tan x = ln (sin x/cos x) = ln I sin x I - ln Icos x I
You have to take absolute value because if sin x and cos x are both negative the ln of the quotient exists but the ln of sin x and cos x don´t

Answer 3

the question is wrong.

right is

ln (tan x) = ln(sin x) - ln(cos x)

this is using ln(a/b) = ln a - ln b
a= sinx and b = cos x gives direcly

ln (sin x/cos x) = ln(sin x) - ln(cos x)
or
ln (tan x) = ln (sin x) - ln (cos x)

Answer 4

It is false
Please give me best answer thanks!