Prove the identity:

\[
\tan 3x - \tan 2x - \tan x = \tan 3x \tan 2x \tan x
\]

tan ( a + b ) = [ tan a + tan b ] / [ 1 - (tan a)*(tan b) ];
let be a = 2x and b = x;
=> tan 3x = [ tan 2x + tan x ] / [ 1 - (tan 2x) (tan x) ] => (tan 3x) [ 1 - (tan 2x)*(tan x) ] =
tan 2x + tan x => tan3x - tan 3xtan 2xtanx = tan 2x + tan x => tan 3x−tan 2x−tanx = tan 3xtan 2xtanx.

Answered by crisforp | 2024-06-10

The identity tan 3 x − tan 2 x − tan x = tan 3 x tan 2 x tan x can be proven by using the tangent addition formula. By substituting and rearranging the terms, we can successfully demonstrate that both sides of the equation are equal. Hence, the identity holds true.
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Answered by crisforp | 2024-12-23