14. Tan 4x + tan 5x - tan 9x = K tan 4x tan 5x tan 9x K=
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Answer:
Step-by-step explanation:
Tan 4x + tan 5x - tan 9x = K tan 4x tan 5x tan 9x ----- (1)
We know that
Tan9x = Tan(4x + 5x) = Tan4x + Tan5x / 1 - Tan4xTan5x
=> Tan9x (1 - Tan4xTan5x) = Tan4x + Tan5x
=> Tan9x - Tan9xTan4xTan5x = Tan4x + Tan5x
=> Tan4x + Tan5x - Tan9x = - Tan9xTan4xTan5x
=> Tan4x + Tan5x - Tan9x = (-1)(Tan9xTan4xTan5x )
Comparing above with (1), we can see that
k = -1
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