How do you simplify cscx/sinx-cosxsecx

I need to know how to simplify this please help me. the / mark stands for division:)

Hi Nicole!

Left side:

Note: csc x = 1/sin x


csc x
-----------
sin x


1
---------------------
sin x * sin x


1
----------------
sin² x


Note: 1/sin x = csc x
Likewise, 1/sin² x = csc² x

1
----------- = csc² x
sin² x


Right side:

Note: sec x = 1/cos x

cos x sec x


cos x * (1/cos x) = 1
(because the cosines cancel each other out)



So, csc x/sin x - cos x sec x
= csc² x - 1


Remember the trig identity: 1 + cot² x = csc² x
Subtract 1 on both sides.

1 - 1 + cot² x = csc² x - 1
cot² x = csc² x - 1

Final Answer: cot² x

Hope this helps!