Friday, October 15, 2010

Prove: sec^2x + csc^2x = sec^2 * csc^2x

proof:
sec^2x + csc^2x
= sec^2x ( 1+ csc^2 x/ sec^2 x)
= sec^2x ( 1+ 1/sin ^2 x /(1/cos ^2x ))
= sec^2 x( 1+ cot^2 x)
= sec ^2 x csc^2 x

3 comments:

  1. You might also note that sec^2+csc^2=(cot+tan)^2 by the pythagorean theorem, seen by looking at their geometric representation on the unit circle. We know cot=cos/sin and tan = sin/cos, by combining them within the parentheses we end up with ((sin^2+cos^2)/cos*sin)^2, but sin^2+cos^2=1, so end up with (1/cos*sin)^2=(sec*csc)^2

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