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- Dec 14, 2005
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Unless I'm doing something wrong here...
sin^2(x) + cos^2(x) = 1
so...
Prove sec^2(x) + csc^2(x) = 1 --
1/sin^2(x) + 1/cos^2(x) = 1
1/(sin^2(x) + cos^2(x)) = 1
1/1 = 1
1 = 1
Thus true.
Now, sub that in
1 = csc^2(x) sec^2(x)
1/sec^2(x) = csc^2(x)
cos^2(x) = csc^2(x)
cos x = csc x
Which is not true.
sin^2(x) + cos^2(x) = 1
so...
Prove sec^2(x) + csc^2(x) = 1 --
1/sin^2(x) + 1/cos^2(x) = 1
1/(sin^2(x) + cos^2(x)) = 1
1/1 = 1
1 = 1
Thus true.
Now, sub that in
1 = csc^2(x) sec^2(x)
1/sec^2(x) = csc^2(x)
cos^2(x) = csc^2(x)
cos x = csc x
Which is not true.