Question

tan4x+tan5x-tan9x=ktan4xtan5xtan9x.then k=?

Answer 1

The formula of tan(a+b) is

$tan(a+b) =\frac{tana+tanb}{1-tanatanb}$

Now 9x can be written as 5x + 4x

we get

tan 9x = tan(5x+4x)

$tan9x=\frac{tan5x+tan4x}{1-tan5xtan4x}$

Cross multiplying we get

tan9x(1-tan5x tan4x) = tan5x + tan4x

tan9x - tan4x tan5x tan9x = tan 5x + tan4x

- tan4x tan5x tan9x = tan5x + tan4x - tan9x

tan 5x + tan4x - tan9x = - tan4x tan5x tan6x

Comparing with

tan 5x + tan4x - tan9x = k tan4x tan5x tan6x

We get

k = -1

Answer 2

Step-by-step explanation:

k= -1

hope this helps you