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Prove that: cos((3pi)/2+x)cos(2x+x)[cot(...

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

Text Solution

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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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