trig
posted by Anonymous .
establish identity
5csc^2theta3cot^2theta=2csc^2theta+3

trig 
Reiny
5 csc^2 Ø  3cot^2 Ø = 2csc^2 Ø + 3
LS = 5/sin^2 Ø  3cos^2 Ø/sin^2 Ø
= (5  3cos^2 Ø)/sin^2 Ø
= (5  3(1  sin^2 Ø) )/sin^2 Ø
= ( 2 + 3sin^2 Ø)/sin^2 Ø
= 2/sin^2 Ø + 3sin^2 Ø/sin^2 Ø
= 2csc^2 Ø + 3
= RS
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