SOLUTION: verify the idenity sec^4x – sec^2x = tan^4x + tan^2x''

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Question 433555: verify the idenity
sec^4x – sec^2x = tan^4x + tan^2x''
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Sec%5E4x+-+Sec%5E2x+=+Tan%5E4x+%2B+Tan%5E2x
To do this one we need the identity 
1%2BTan%5E2theta=Sec%5E2theta and its rearranged version Sec%5E2theta-1=Tan%5E2theta

Sec%5E4x+-+Sec%5E2x+=+Tan%5E4x+%2B+Tan%5E2x

Factor common factor Sec%5E2x out of the left side

Sec%5E2x%28Sec%5E2x-1%29+=+Tan%5E4x+%2B+Tan%5E2x

Replace the first factor on the left, Sec%5E2x, by 1%2BTan%5Ex

Replace the second factor on the left, %28Sec%5E2-1%29 by Tan%5E2x


%281%2BTan%5E2x%29%28Tan%5E2x%29+=+Tan%5E4x+%2B+Tan%5E2x

Multiply the left side out:

Tan%5E2x+%2B+Tan%5E4x+=Tan%5E4x+%2B+Tan%5E2x

Reverse the terms on the left

Tan%5E4x+%2B+Tan%5E2x+=Tan%5E4x+%2B+Tan%5E2x

Edwin