Simplify
(tan 4X+tan 2x)/(1-(tan 4X)(tan2X))
This is clearly tan(4x+2x) = tan(6x)
To simplify the expression, we can make use of the trigonometric identity:
tan(A + B) = (tan A + tan B) / (1 - tan A * tan B)
In this case, A = 4X and B = 2X, so we can rewrite the expression as:
(tan 4X + tan 2X) / [1 - (tan 4X)(tan 2X)]
Now, we can substitute A and B into the identity:
tan(4X + 2X) = (tan 4X + tan 2X) / [1 - (tan 4X)(tan 2X)]
Simplifying further:
(tan 6X) / [1 - (tan 4X)(tan 2X)]
Therefore, the simplified expression is (tan 6X) / [1 - (tan 4X)(tan 2X)].