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Question

Show that:  $$\tan { 3x } .\tan { 2x } .\tan { x } =\tan { 3x } -\tan { 2x } -\tan { x } $$.


Solution

$$\Rightarrow$$  Let us take, $$\tan(3x)=\tan(x+2x)$$ 

$$\Rightarrow$$  $$\tan(A+B)=\dfrac{\tan(A)+\tan(B)}{1-\tan\,A.\tan\,B}$$

$$\tan(3x)=\dfrac{\tan(x)+\tan(2x)}{1-(\tan(x)\tan(2x))}$$

$$\therefore$$  $$\tan(3x)-\tan(x).\tan(2x).\tan(3x)=\tan(x)+\tan(2x)$$

$$\therefore$$    $$\tan(3x).\tan(2x).\tan(x)=\tan(3x)-\tan(2x)-\tan(x)$$

Physics

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