tan 2x- tan 6y/ 1+ tan 2x tan 6y
recall that tan(A-B) = (tanA-tanB)/(1+tanAtanB)
To simplify the given expression, we can use the trigonometric identity:
tan(a - b) = (tan a - tan b) / (1 + tan a tan b)
Let's rewrite the given expression using this identity:
tan 2x - tan 6y / (1 + tan 2x tan 6y)
Now, by comparing this with the trigonometric identity, we have:
a = 2x
b = 6y
So, we can replace a and b in the identity:
tan(2x - 6y) / (1 + tan 2x tan 6y)
Hence, the simplified expression is tan(2x - 6y) / (1 + tan 2x tan 6y).