Answer:
The given expressions simplifies to tan (4x).
Step-by-step explanation:
Here, the given expression is : [tex]\frac{tan9x - tan5x}{1+ tan9xtan5x}[/tex]
By TRIGONOMETRIC IDENTITY:
[tex]tan (A-B) = \frac{tanA - tanB}{1+ tanAtanB}[/tex]
Putting this identity here, and taking A = 9 x, B = 5 x, we get
[tex]\frac{tan9x - tan5x}{1+ tan9xtan5x} = tan (9x-5x)[/tex]
= tan(4x)
Hence, the given expressions simplifies to tan (4x).
