You can put this solution on YOUR website! How to prove the identity
(7csc^2x-25cscx-12)/(cscx-4) = (7)/(sinx) +3
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start with left side:
(7csc^2x-25cscx-12)/(cscx-4)
factor
(7cscx+3)(cscx-4)/(cscx-4)
=(7cscx+3)
=7(1/sinx)+3
=(7/sinx)+3
verified: left side=right side