1.

If`(sin^3theta-cos^3theta)/(sin theta-cos theta)-cos theta/sqrt(1+cot^2theta)-2tan theta.cot theta=-1`

Answer» `L.H.S. = (sin^3theta-cos^3theta)/(sintheta-costheta) - costheta/(sqrt(1+cot^2theta)) - 2tanthetacot theta`
`=((sintheta-costheta)(sin^2theta+cos^2theta+sinthetacostheta))/(sintheta-costheta) - costheta/(sqrt(cosec^2theta)) - 2tantheta(1/tantheta)`
`=(1+sinthetacostheta) -costheta/(cosec theta) -2`
`=1+sinthetacostheta - costhetasintheta -2 `
`=1-2 =-1 = R.H.S.`


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