CBSE (Science) Class 11CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

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

Login
Create free account


      Forgot password?

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 .

  Is there an error in this question or solution?

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.
S
View in app×