If `cos e ctheta-sintheta=l` and `sectheta-costheta=m ,` prove that `l^2m^2(l^2+m^2+3)=1`

Explanation

Given,

`cosectheta-sintheta=l`
and `sectheta-costheta=m ,`

now,

`l^2m^2(l^2+m^2+3)`

`=(cosectheta-sintheta)^2(sectheta-costheta)^2((cosectheta-sintheta)^2+(sectheta-costheta)^2+3)`


`=(1/(sintheta)-sintheta)^2(1/(costheta)-costheta)^2((1/(sintheta)-sintheta)^2+(1/(costheta)-costheta)^2+3)`
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