SOLUTION: sec^4 A-sec^2 A is equal to what? thankyou

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Question 775431: sec^4 A-sec^2 A is equal to what?
thankyou
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
sec%5E4+%28A%29-sec%5E2+%28A%29
sec%5E2+%28A%29%28+sec%5E2+%28A%29-1%29..........since sec%5E2%28A%29+=+%281%2F%28cos%28A%29%29%29%5E2, we have
sec%5E2+%28A%29%28%281%2F%28cos%28A%29%29%29%5E2-1%29+

sec%5E2%28A%29%281%2Fcos%5E2%28A%29-1%29+

sec%5E2+%28A%29%281%2Fcos%5E2%28A%29-cos%28A%29%5E2%2Fcos%5E2%28A%29%29

sec%5E2+%28A%29%28%281-cos%5E2%28A%29%29%2Fcos%5E2%28A%29%29 ...since 1-cos%5E2%28A%29=sin%5E2%28A%29, we have

sec%5E2+%28A%29%28sin%5E2%28A%29%29%2Fcos%5E2%28A%29%29

sec%5E2+%28A%29tan%5E2%28A%29