Question

If x= sin theta then x/√1-x^2 is​

Answer 1

Well,

Given that
`x=\sin(\theta)`,

We can rewrite the equation like,

`(\sin(\theta))/(√(1-\sin(\theta)^2))`

Now use,
`\cos(\theta)^2+\sin(\theta)^2=1` which implies that
`1-\sin(\theta)^2=\cos(\theta)^2`

That means that,

`(\sin(\theta))/(√(1-\sin(\theta)^2))\Longleftrightarrow(\sin(\theta))/(√(\cos(\theta)^2))`

By def
`√(x^2)=x` therefore
`√(\cos(\theta)^2)=\cos(\theta)`

So the fraction now looks like,

`(\sin(\theta))/(\cos(\theta))`

Which is equal to the identity,

`\boxed{\tan(\theta)}=(\sin(\theta))/(\cos(\theta))`

Hope this helps.

r3t40