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# Prove that Tan a + Tan B Tan a − Tan B = Sin ( a + B ) Sin ( a − B ) - CBSE (Science) Class 11 - Mathematics

ConceptTrigonometric Functions of Sum and Difference of Two Angles

#### Question

Prove that
$\frac{\tan A + \tan B}{\tan A - \tan B} = \frac{\sin \left( A + B \right)}{\sin \left( A - B \right)}$

#### Solution

$LHS = \frac{\tan A + \tan B}{\tan A - \tan B}$
$= \frac{\frac{\sin A}{\cos A} + \frac{\sin B}{\cos B}}{\frac{\sin A}{\cos A} - \frac{\sin B}{\cos B}}$
$= \frac{\frac{\sin A \cos B + \cos A\sin B}{\cos A \cos B}}{\frac{\sin A \cos B - \cos A \sin B}{\cos A \cos B}}$
$= \frac{\sin A \cos B + \cos A \sin B}{\sin A \cos B - \cos A \sin B}$
$= \frac{\sin\left( A + B \right)}{\sin\left( A - B \right)}$
= RHS
Hence proved .

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#### APPEARS IN

RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 7: Values of Trigonometric function at sum or difference of angles
Ex.7.10 | Q: 10 | Page no. 19
Solution Prove that Tan a + Tan B Tan a − Tan B = Sin ( a + B ) Sin ( a − B ) Concept: Trigonometric Functions of Sum and Difference of Two Angles.
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