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
it's complicated but ok...
ReplyDeleteyeah awful explanation
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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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