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prove that siny*cosy*tany=1-cos^2y
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We'll manage the left side writting `tan y = sin y/cos y` .
We'll re-write the given expression:
`sin y*cos y*(siny/cosy) = 1 - cos^2 y`
We'll simplify by cos y to the left side:
`sin y*sin y = 1 - cos ^2 y`
`sin^2 y = 1 - cos ^2 y`
We'll add `cos^2 y ` both sides:
`sin^2 y + cos^2 y = 1`
Since we've get the Pythagorean identity, the given expression represents an identity.
Posted by giorgiana1976 on August 30, 2011 at 12:09 AM (Answer #1)
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