establish identity

Question

5csc^2theta-3cot^2theta=2csc^2theta+3

Answer 1

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