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Question
Prove that:
tan 13x − tan 9x − tan 4x = tan 13x tan 9x tan 4x
Solution
\[\text{ We know that }13x = 9x + 4x\]
Therefore,
\[ \tan\left( 13x \right) = \tan\left( 9x + 4x \right)\]
\[ \Rightarrow \tan13x = \frac{\tan9x + \tan4x}{1 - \tan9x \tan4x}\]
\[ \Rightarrow \tan13x - \tan13x \tan9x \tan 4x = \tan9x + \tan4x\]
\[ \Rightarrow \tan13x - \tan9x - \tan4x = \tan13x \tan9x \tan4x \]
Hence proved .
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