We have
`"LHS "= (1+cot theta - "cosec" theta )(1+ tan theta +sec theta ) `
` =(1+(cos theta)/(sin theta) -(1)/(sin theta ))(1+ (sin theta)/(cos theta) +(1)/(cos theta))`
` =((sin theta +cos theta -1))/(sin theta)*((cos theta+ sin theta +1))/(cos theta )`
` =([(sin theta +cos theta)-1]*[(sin theta+cos theta)+1])/(sin theta cos theta)`
` =((sin theta + cos theta)^(2)-1)/(sin theta cos theta )`
` =(sin^(2) theta + cos ^(2) theta +2 sin theta cos theta -1)/(sin theta cos theta)`
` =(1+2sin theta cos theta -1)/(sin theta cos theta ) " "[ because sin^(2)theta + cos ^(2) theta =1 ] `
` =(2sin theta cos theta)/(sin theta cos theta )=2="RHS." `
` therefore "LHS " = "RHS. " `
