SOLUTION: Solve an interval {hint: [0,2pie)} sinx + cosxcotx= 1/sinx?

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Question 65309: Solve an interval {hint: [0,2pie)} sinx + cosxcotx= 1/sinx?
Answer by amran(4) About Me  (Show Source):
You can put this solution on YOUR website!
Ans: x can take any value because the expression is an identity.
Proof:
LHS = +sin%28x%29+%2B+cos%28x%29cot%28x%29+
= +sin%28x%29+%2B+cos%28x%29cos%28x%29%2Fsin%28x%29+
= +sin%28x%29+%2B+%28cos%28x%29%29%5E2+%2Fsin%28x%29+
= +%28%28sin%28x%29%29%5E2+%2B+%28cos%28x%29%29%5E2%29%2Fsin%28x%29+
= +1%2Fsin%28x%29+
= RHS