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Expert: - 5/15/2007


Question
Hello Mr. I need some help, I have no idea how to do this.

1 - cos2x sec(squared)x = tan(squared)x

a "hint" would be to work only the left side of the eq. to obtain tan(squared)x = tan(squared)x ?

Answer
use cos(2x) = cos^2(x) - sin^2(x) and sec^2(x) = 1/cos^2(x)

substitute these into the left side and get

1 - (cos^2(x) - sin^2(x))(1/cos^2(x)) =

1 - ( 1 - sin^2(x)/cos^2(x) ) =

1 - 1 + sin^2(x)/cos^2(x) =

tan^2(x)


this verifies the identity

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