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Original Equation

sec2(x) = 1 + tan2(x)Leave the left side assec2(x) and for the proof, try to make the right side equal the left side.

We know tan = sin/cos

1 + tan2(x) = 1 + sin2(x)/cos2(x)


Rewrite the 1 in terms of cos2(x)

1 + sin2(x)/cos2(x) = cos2(x)/cos2(x) + sin2(x)/cos2(x)


Simplify, now that the denominators have the same terms

cos2(x)/cos2(x) + sin2(x)/cos2(x) = [ cos2(x) + sin2(x) ] / cos2(x)


Use the trig. identity: cos2(x) + sin2(x) = 1

[ cos2(x) + sin2(x) ] / cos2(x) = 1 / cos2(x)


Remember 1/cosine is equal to secant.\

1 / cos2(x) = sec2(x)


Recall, the left side the equation was: sec2(x)
The right side (we just solved for is): sec2(x)


sec2(x) = sec2(x)
Left side = right side, Q.E.D.


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โˆ™ 2013-04-05 09:10:08
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