# Thread: Using Basic identities to simply the expression

1. ## Using Basic identities to simply the expression

Problem:

cos^2(x) / sin^2(x) + csc(x)sin(x)

I've worked on it,
On the right of the + sign I changed the csc(x) into 1/sin(x)
so...
cos^2(x) / (sin^2(x)) + 1/sin(x) * sin(x)
cos^2(x) / (sin^2(x)) + 1
1/sec^2(x) / (sin^2(x)) +1
1/sec^2(x) / (1/ csc^2(x)) + 1

then i dont know where to go from there...

2. Originally Posted by yeunju
Problem:

cos^2(x) / sin^2(x) + csc(x)sin(x)

I've worked on it,
On the right of the + sign I changed the csc(x) into 1/sin(x)
so...
cos^2(x) / (sin^2(x)) + 1/sin(x) * sin(x)
cos^2(x) / (sin^2(x)) + 1
1/sec^2(x) / (sin^2(x)) +1
1/sec^2(x) / (1/ csc^2(x)) + 1

then i dont know where to go from there...
Hi yeunju,

Here's what I did:

$\displaystyle \frac{\cos^2 x}{\sin^2 x}+\csc x \sin x$

$\displaystyle \frac{\cos^2 x}{\sin^2 x}+\frac{1}{\sin x}(\sin x)$

$\displaystyle \frac{\cos^2 x}{\sin^2 x}+1$

$\displaystyle \frac{\cos^2 x+ \sin^2 x}{\sin^2 x}$

$\displaystyle \frac{1}{\sin^2 x}$

$\displaystyle \csc^2 x$