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Prove that Tan 69 ∘ + Tan 66 ∘ 1 − Tan 69 ∘ Tan 66 ∘ = − 1 . - Mathematics

Answer in Brief

Prove that \[\frac{\tan 69^\circ + \tan 66^\circ}{1 - \tan 69^\circ \tan 66^\circ} = - 1\].

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Solution

\[\text{ LHS }= \frac{\tan69^\circ + \tan66^\circ}{1 - \tan69^\circ\tan66^\circ}\]
\[ = \tan\left( 69^\circ + 66^\circ \right) \left[\text{ Using the formula }\frac{\tan A + \tan B}{1 - \tan A\tan B} = \tan\left( A + B \right) \right]\]
\[ = \tan135^\circ\]
\[ = \tan\left( 180^\circ - 45^\circ \right)\]
\[ = - \tan45^\circ \left[ \tan\left( 180 - A \right) = - \tan A \right]\]
\[ = - 1\]
 = RHS
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 13 | Page 19
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