SOLUTION: Prove as an identity; ((sin(2x)) / (sin(x))) - ((cos(2x)) / (cos(x))) = sec(x)

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Question 756972: Prove as an identity;
((sin(2x)) / (sin(x))) - ((cos(2x)) / (cos(x))) = sec(x)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Prove as an identity;
((sin(2x)) / (sin(x))) - ((cos(2x)) / (cos(x))) = sec(x)
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Start with LHS
((sin(2x)) / (sin(x))) - ((cos(2x)) / (cos(x)))
(2sinxcosx)/(sinx)-(cos^2x/cosx)
(2cosx)-(cos^2x-sin^x)/cosx)
(2cosx)-(cos^2x-(1-cos^2^x)/cosx)
(2cosx)-(-1+2cos^2x)/cosx)
(2cosx)+(1-2cos^2x)/cosx)
(2cosx)+(1/cos-2cosx)
1/cosx=secx
verified:LHS=RHS