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The value of the equation tan^6(20^@)-33...

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

Text Solution

Verified by Experts

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`
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The value of the expression (tan^(2)20^(0)-sin^(2)20^(@))/(tan^(2)20^(0)+sin^(2)20^(@)) is

tan20^(@)+2tan50^(@)=

3tan^6 10^@-27tan^4 10^@+33tan^2 10^@=