Question

Simplify tan9x-tan5x / 1+tan9xtan5x​

Answer 1

Answer:

The given expressions simplifies to tan (4x).

Step-by-step explanation:

Here, the given expression is : $\frac{tan9x - tan5x}{1+ tan9xtan5x}$

By TRIGONOMETRIC IDENTITY:

$tan (A-B) = \frac{tanA - tanB}{1+ tanAtanB}$

Putting this identity here, and taking A = 9 x, B = 5 x, we get

$\frac{tan9x - tan5x}{1+ tan9xtan5x} = tan (9x-5x)$

= tan(4x)

Hence, the given expressions simplifies to tan (4x).