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If sintheta-costheta=3^(1/2), then the v...

If `sintheta-costheta=3^(1/2)`, then the value of `sin^3theta-cos^3theta` is __________ .

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The correct Answer is:
1
`sintheta-costheta=1`
`orsin^2theta+cos^2theta-2sinthetacostheta=1`
`or sinthetacostheta=0`
Now `sin^3theta-cos^3theta=1(sin^2thta+cos^2theta+sinthetacostheta)`
`=(sintheta-costheta)^2+3sinthetacostheta`
`=1+3sinthetacostheta=1`
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