SOLUTION: Can you please help me thanks alot Reduce (csc^ x - sec^ x) to an expression containing only tan x.

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Question 205006: Can you please help me thanks alot
Reduce (csc^ x - sec^ x) to an expression containing only tan x.

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Can you please help me thanks alot
Reduce %28csc%5E2x+-+sec%5E2x%29 to an expression containing only tan%28x%29.

The two identities we have involving cosecant and secant are

1+%2B+Tan%5E2phi=sec%5E2phi and 1+%2B+Cot%5E2phi=csc%5E2phi

Using them we have

%28csc%5E2x+-+sec%5E2x%29
1%2BCot%5E2x+-+%281%2BTan%5E2x%29
1%2BCot%5E2x+-+1-Tan%5E2x
Cot%5E2x-Tan%5E2x

Now we can get use the identity Cot%28phi%29=1%2FTan%28phi%29 
to get the term in cotangent in terms of tangent:

1%2F%28Tan%5E2x%29-Tan%5E2x

That's actually good enough there, but maybe your teacher
wants you to combine those terms:


1%2F%28Tan%5E2x%29-Tan%5E2x
1%2F%28Tan%5E2x%29-%28Tan%5E2x%29%2F1
1%2F%28Tan%5E2x%29-%28Tan%5E2x%29%28Tan%5E2x%29%2F%281%28Tan%5E2x%29%29

1%2F%28Tan%5E2x%29-%28Tan%5E4x%29%2F%28Tan%5E2x%29

%281-Tan%5E4x%29%2F%28Tan%5E2x%29

Edwin