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Question
Prove the following:
`tan 4x = (4tan x(1 - tan^2 x))/(1 - 6tan^2 x + tan^4 x)`
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Solution
`tan4 = tan 2 (2x) = (2tan2x)/(1 - tan^2 2x)`
= `(2tan 2x)/(1 - tan^2 (2x))`
= `((2tanx)/(1 - tan^2x))/(1 - (2tan^x)/(1 - tan^2x) `
= `(4tanx (1 - tan^2 x))/((1 - tan^2x)^2 - 4 tan^2 x)`
= `(4tanx ( 1 - tan^2 x))/(1 - 2 tan^2x+ tan^2 x - 4tan^2`
= `(4tanx (1 - tan^2x))/(1 + tan^4 x - 6 tan^2x)`
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