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Prove That:Tan 8x − Tan 6x − Tan 2x = Tan 8x Tan 6x Tan 2x - Mathematics

Short Note

Prove that:
tan 8x − tan 6x − tan 2x = tan 8x tan 6x tan 2x

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Solution

We know that 8x = 6x + 2x
Therefore, 
\[ \tan\left( 8x \right) = \tan\left( 6x + 2x \right)\]
\[ \Rightarrow \tan\left( 8x \right) = \frac{\tan6x + \tan2x}{1 - \tan6x \tan2x}\]
\[ \Rightarrow \tan8x - \tan8x \tan6x \tan2x = \tan6x + \tan2x\]
\[ \Rightarrow \tan8x - \tan6x - \tan2x = \tan8x \tan6x \tan2x\]
Hence proved.

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 7 Values of Trigonometric function at sum or difference of angles
Exercise 7.1 | Q 17.1 | Page 20
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