If x= sin theta then x/√1-x^2 is

Question

asked May 26, 2020 169k views

1 Answer

Jerome Dalbert · Answer 1 · 2020-05-31T23:51:39+0000

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