Ask Me Help Desk - Prove 8csc^2x-3cot^2=3+5csc^2

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Prove 8csc^2x-3cot^2=3+5csc^2

I have to prove how one side can equal the other but i do not know where to begin with this problem.

I know CSC= 1/sin and COT= cos/sin
I know all of the pythagorean identities as well but i still do not know where to begin with this problem.

As usual, first convert the csc and cot functions to their sin and cos equivalents. The trick is then to look for opportunities to use those Pythagorian identities. I'll get you started: note the left hand side is:

$\frac 8 {\sin^2x}-\frac {3 \cos^2x}{\sin^2x}$

which is equivalent to:

$\frac {8 - 8 \cos^2x +5 \cos^2x}{\sin^2x}$

Do you see the opportunity to apply $1-\cos^2x = \sin^2x$ ?

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