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Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)...

Prove that `(4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot`

Text Solution

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We have `cos 3x=4 cos^(3)x-3 cos x`. Hence.
`4cos ^(2)x-3=(cos3x)/(cos x)` for all `xne(2k+1).(pi)/(2), k in z`.
`therefore (4 cos ^(2)9^(@)-3)(4 cos^(2)27^(@)-3)=(cos27^(@))/(cos9^(@)).(cos 81^(@))/(cos 27^(@))` ltbr. `=(cos 81^(@))/(cos9^(@))`
`=(sin 9^(@))/(cos9^(@))=tan 9^(@)`
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