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