If a + B = C, Then Write the Value of Tan a Tan B Tan C. - Mathematics

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If A + B = C, then write the value of tan A tan B tan C.

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$\tan A \tan B \tan C = \tan A \tan B \tan (A + B) [Using A + B = C]$
$= \tan A \tan B \times \frac{\tan A + \tan B}{1 - \tan A \tan B}$
$= \frac{\tan^{2} A \tan B + \tan A \tan^{2} B}{1 - \tan A \tan B}$
$= \frac{\tan^{2} A \tan B + \tan A \tan^{2} B + \tan A + \tan B - \tan A - \tan B}{1 - \tan A \tan B}$
$= \frac{- \tan A (1 - \tan A \tan B) - \tan B (1 - \tan A \tan B) + \tan A + \tan B}{1 - \tan A \tan B}$
$= \frac{- (1 - \tan A \tan B) (\tan A + \tan B) + \tan A + \tan B}{1 - \tan A \tan B}$
$= \frac{\tan A + \tan B}{1 - \tan A \tan B} - \tan A - \tan B$
$= \tan (A + B) - \tan A - \tan B$
$= \tan C - \tan A - \tan B$

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Trigonometric Functions of Sum and Difference of Two Angles

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Q 10 Q 9 Q 11

पाठ 7: Values of Trigonometric function at sum or difference of angles - Exercise 7.3 [पृष्ठ २७]

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आरडी शर्मा Mathematics [English] Class 11

पाठ 7 Values of Trigonometric function at sum or difference of angles
Exercise 7.3 | Q 10 | पृष्ठ २७

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Trigonometric Functions of Sum and Difference of Two Angles

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If a + B = C, Then Write the Value of Tan a Tan B Tan C. - Mathematics

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