# 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

#### 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.

Is there an error in this question or solution?

#### 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