Question

Identify the expression that completes the equation so that it is an identity
cosx / 1-sinx =


a) 1+cscx / cscx
b) sinx
c) 1+sinx / cosx
d) 1+secx / secx

I think there's an identity that 1-sinx/sinx = 1 or something right? I just can't find the identity to help me out with this one.

Answer 1

There is something called as rationalising the denominator.
Any idea about that?

Answer 2

As in taking the square root of the expression? Haven't tried it with this material.. :0

Answer 3

I'll explain with an example -

\[\frac{ \cos x }{ 1-\sin x } x \frac{ 1+\sin x }{ 1+\sin x }\]

Answer 4

This is called rationalising the denominator.

Basically you can convert the denominator to a different proper form then.

Am sure you know that (1-sin x)(1+sin x) = 1 - sin^2x?

Answer 5

oh okay, yeah I remember this. well, rationalizing.

As for the identity... now I know that, haha. New to me.

Answer 6

would it be 1+sinx/ cosx then? since it's flipped..

Answer 7

@cmolina19 do you know how to get a conjugate of a binomial?

Answer 8

@cmolina19 yes ^ ans is correcto