[tex] \frac{tan@-cot@}{
[email protected]@}= tan^{2}@- cot^{2}@[/tex]
LHS= [tex] \frac{tan@-cot@}{
[email protected]@} = \frac{tan@- \frac{1}{tan@} }{
[email protected]@} [/tex]
[tex]= \frac{ tan^{2}@-1 }{
[email protected]@.cos@} = \frac{ tan^{2}@-1 }{tan@ \frac{sin@}{cos@}
[email protected]@} [/tex]
[tex]= \frac{( tan^{2}@-1) sec^{2}@ }{ tan^{2}@ } = \frac{( tan^{2}@-1)( tan^{2}@+1) }{ tan^{2}@ } [/tex]
[tex]= \frac{ tan^{4}@-1 }{ tan^{2}@ } = \frac{ tan^{4}@ }{ tan^{2}@ } - \frac{1}{ tan^{2}@ } [/tex]
[tex]= tan^{2}@- cot^{2}@ = R.H.s[/tex]
