SOLUTION: Verify that secθ/sinθ (times) cotθ/cscθ is an identity

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Question 174392: Verify that secθ/sinθ (times) cotθ/cscθ is an identity
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Using phi because θ won't render in the formula generator

%28sec%28phi%29%2Fsin%28phi%29%29%28cot%28phi%29%2Fcsc%28phi%29%29 cannot be an identity because you haven't set it equal to anything.

Now if you had said, "Verify that %28sec%28phi%29%2Fsin%28phi%29%29%28cot%28phi%29%2Fcsc%28phi%29%29=csc%28phi%29 is an identity," we could do that.

%28sec%28phi%29%2Fsin%28phi%29%29%28cot%28phi%29%2Fcsc%28phi%29%29

Since sin%28alpha%29=1%2Fcsc%28alpha%29, sin%28alpha%29csc%28alpha%29=1, so:


%28sec%28phi%29%2Fsin%28phi%29%29%28cot%28phi%29%2Fcsc%28phi%29%29=sec%28phi%29cot%28phi%29, but we also know that:

cot%28alpha%29=cos%28alpha%29%2Fsin%28alpha%29, so

sec%28phi%29cot%28phi%29=sec%28phi%29%28cos%28phi%29%2Fsin%28phi%29%29. Furthermore, we know that:

Since cos%28alpha%29=1%2Fsec%28alpha%29, cos%28alpha%29sec%28alpha%29=1, so:

sec%28phi%29%28cos%28phi%29%2Fsin%28phi%29%29=1%2Fsin%28phi%29=csc%28phi%29.

Hope that helps.