SOLUTION: prove {{{sin^2(theta)=(1/2)(1-cos2(theta))}}} is an identity

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Question 882956: prove sin%5E2%28theta%29=%281%2F2%29%281-cos2%28theta%29%29 is an identity
Answer by Leaf W.(135) About Me  (Show Source):
You can put this solution on YOUR website!
Hello!
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Since the right side is more complicated, let us work from the right and try to get to the left side.
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Use the trig identity cos%282theta%29+=+cos%5E2%28theta%29+-+sin%5E2%28theta%29 and simplify:
sin%5E2%28theta%29=%281%2F2%29%281+-+cos%282theta%29%29
sin%5E2%28theta%29=%281%2F2%29%281+-+%28cos%5E2%28theta%29+-+sin%5E2%28theta%29%29%29
sin%5E2%28theta%29=%281%2F2%29%281+-+cos%5E2%28theta%29+%2B+sin%5E2%28theta%29%29
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Since sin%5E2%28theta%29+%2B+cos%5E2%28theta%29+=+1, sin%5E2%28theta%29+=+1+-+cos%5E2%28theta%29, so use this to substitute 1+-+cos%5E2%28theta%29 for sin%5E2%28theta%29 and simplify:
sin%5E2%28theta%29=%281%2F2%29%281+-+cos%5E2%28theta%29+%2B+sin%5E2%28theta%29%29
sin%5E2%28theta%29=%281%2F2%29%28sin%5E2%28theta%29+%2B+sin%5E2%28theta%29%29
sin%5E2%28theta%29=%281%2F2%29%282sin%5E2%28theta%29%29
sin%5E2%28theta%29=sin%5E2%28theta%29
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Yay! Both sides of the equation are the same, so you have verified the identity!
Let me know if you need any further clarification. =)