Question

निम्नलिखित को सिद्ध कीजिए:

`tan 4x = (4tan x(1 - tan^2 x))/(1 - 6tan^2 x + tan^4 x)`

Answer 1

`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)`