rewrite:
tan 4 X + tan 2 X/ 1 - (tan4X)(tan2X)
since tan(A+B) = (tanA+tanB)/(1-tanAtanB),
I'd say you have tan(4X+2X) = tan6X
To rewrite the expression tan(4X) + tan(2X) / [1 - (tan(4X))(tan(2X))], let's break it down step by step:
Step 1: Simplify the numerator
The numerator is tan(4X) + tan(2X). To simplify this, we can use the identity tan(A+B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B)).
In this case, A = 2X and B = 2X. So, we can rewrite the numerator as tan(2X + 2X) = tan(4X).
Step 2: Simplify the denominator
The denominator is 1 - (tan(4X))(tan(2X)). Again, we can use the tangent addition formula to simplify this. The formula is 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 denominator as 1 - tan(4X + 2X) = 1 - tan(6X).
Step 3: Simplify the expression
Now that we have simplified the numerator and denominator separately, we can rewrite the entire expression as tan(4X) / (1 - tan(6X)).
So, the rewritten expression is tan(4X) / (1 - tan(6X)).