1.

`cos((3pi)/(2) +x) cos(2pi+x)[cot(3pi)/(2)-x+cot(2pi+x)]=1`

Answer» LHS `=cos((3pi)/(2)+x)cos(2pi+x)[(cos(3pi)/(2)-x)+cot(2pi+x)]`
`=sinx.cosx[tanx+cotx]`
`sinx.cosx[(sinx)/(cosx)+(cosx)/(sinx)]`
`=sin^(2)x+cos^(2)x=1`= R.H.S Hence Proved.


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