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Prove That: Tan 36° + Tan 9° + Tan 36° Tan 9° = 1 - Mathematics

Short Note

Prove that:
tan 36° + tan 9° + tan 36° tan 9° = 1

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Solution

\[\text{ We know that }36^\circ + 9^\circ = 45^\circ\]
Therefore, 
\[ \tan\left( 36^\circ + 9^\circ \right) = \tan45^\circ\]
\[ \Rightarrow \frac{\tan36^\circ + \tan9^\circ}{1 - \tan36^\circ \tan9^\circ} = 1\]
\[ \Rightarrow \tan36^\circ + \tan9^\circ = 1 - \tan36^\circ \tan9^\circ\]
\[ \Rightarrow \tan36^\circ + \tan9^\circ + \tan36^\circ \tan9^\circ = 1\]
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 17.3 | Page 20
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