Super confused need help asap. Am I right or am I losing my mind?

Question

#(cos^2/sin^2X)(1/sin^2X)#

Doesn't this equal #cos^2x/sin^4x# I could've sworn someone told me to multiply the two denominators together or I might be going crazy. I need an answer asap.

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Answer 1 · 2018-02-06T01:57:46

That makes total sense what you did. Let's just check to see if we can somehow simplify further.

Recall that #cos^2x +sin^2x =1#:

#(1 - sin^2x)/sin^4x#

#1/sin^4x - 1/sin^2x#

#csc^4x - csc^2x#

Or we can rewrite as #cot^2xcsc^2x# because #cottheta = costheta/sintheta# and #cscx = 1/sinx#

Hopefully this helps!