Check whether the following equation `tan^(4)theta+tan^(6)theta=tan^(3)thetasec^(2)theta` is an identity or not ?

Explanation

Given equation ,
`tan^(4)0+tan^(6)theta=tan^(3)thetasec^(2)theta`
`rArrtan^(4)theta(1+tan^(2)theta)=tan^(3)thetasec^(2)theta`
`rArrtan^(4)thetasec^(2)theta=tan^(3)thetasec^(2)theta`
`:' L.H.S.neR.H.S`.
`:.` It is not an identity.
Again , `tan^(4)thetasec^(2)theta-tan^(3)thetasec^(2)theta=0`
`rArrtan^(3)thetasec^(2)theta(tantheta-1)=0`
`rArrtan^(3)theta=0orsec^(2)theta=0ortantheta-1=0`
`rArrtantheta=0orsec^(2)theta=0ortantheta=1`
but`sec^(2)theta=1+tan^(2)thetagt0ne0`
and `tantheta=0rArrtheta=0^(@)`
and `tantheta=0rArrtheta=45^(@)`
`:.theta=0^(@)andtheta45^(@)`
Therefore , given equation satisfies only for `theta=0^(@)andtheta=45^(@)`.
`rarr`Given equation os not an identity.
Alternate Method :For `theta=60^(@)`
L.H.S.`=tan^(4)60^(@)+tan^(6)60^(@)`
`=(sqrt(3))^(4)+(sqrt(3))^(6)=9+27=36`
and R.H.S. `=tan^(3)60^(@)*sec^(2)60^(@)`
`=(sqrt(3))^(3)(2)^(2)=12sqrt(3)`
`:.` L.H.S.`ne` R.H.S.
`rArr` Given equation is not an identity.