Question

The value of the equation `tan^6(20^@)-33tan^4(20^@)+27tan^2(20^@)` is :

Answer 1

We know, `tan 60^@ = sqrt3`
`=> tan(3**20^@) = sqrt3`
`=>(3tan20^@-tan^3 20^@)/(1-3tan^2 20^@) = sqrt3`
`=>((3tan20^@-tan^3 20^@)/(1-3tan^2 20^@))^2 = 3`
`=>9tan^2 20^@ + tan^6 20^@ - 6tan^4 20^@ = 3(1+9tan^2 20^@ - 6tan^2 20^@)`
`=>9tan^2 20^@ + tan^6 20^@ - 6tan^4 20^@ = 3+27tan^2 20^@ - 18tan^2 20^@`
`=>tan^6 20^@ - 33 tan^4 20^@ + 27 tan^2 20^@ = 3`