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If Tan a = 5 6 and Tan B = 1 11 , Prove that a + B = π 4 . - CBSE (Science) Class 11 - Mathematics

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Question

 If \[\tan A = \frac{5}{6}\text{ and }\tan B = \frac{1}{11}\], prove that \[A + B = \frac{\pi}{4}\].

Solution

We have: 
\[\tan A = \frac{5}{6}\text{ and }\tan B = \frac{1}{11}\]
\[\text{ Therefore, }\tan\left( A + B \right) = \frac{\tan A + \tan B}{1 - \tan A \tan B}\]
\[ \Rightarrow \tan\left( A + B \right) = \frac{\tan A + \tan B}{1 - \tan A \tan B}\]
\[ \Rightarrow \tan\left( A + B \right) = \frac{\frac{5}{6} + \frac{1}{11}}{1 - \frac{5}{6} \times \frac{1}{11}}\]
\[ \Rightarrow \tan\left( A + B \right) = \frac{\frac{61}{66}}{\frac{61}{66}}\]
\[ \Rightarrow \tan\left( A + B \right) = 1\]
\[ \Rightarrow \tan\left( A + B \right) = \tan\left( \frac{\pi}{4} \right)\]
\[\text{ Therefore, }A + B = \frac{\pi}{4} . \]
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: 14.1 | Page no. 20
Solution If Tan a = 5 6 and Tan B = 1 11 , Prove that a + B = π 4 . Concept: Trigonometric Functions of Sum and Difference of Two Angles.
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