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If Tan (A + B) = X and Tan (A − B) = Y, Find the Values of Tan 2a and Tan 2b. - CBSE (Science) Class 11 - Mathematics

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Question

If tan (A + B) = x and tan (A − B) = y, find the values of tan 2A and tan 2B.

 

Solution

\[\tan(2A) = \tan(A + A)\]
\[ = \tan(A + B + A - B)\]
\[ = \frac{\tan(A + B) + \tan(A - B)}{1 - \tan(A + B)\tan(A - B)}\]
\[ = \frac{x + y}{1 - xy}\]

\[\tan 2B = \tan \left( B + B \right)\]

\[ = \tan \left( B + A + B - A \right)\]

\[ = \frac{\tan \left( A + B \right) + \tan \left( B - A \right)}{1 - \tan\left( A + B \right)\tan\left( B - A \right)}\]

\[ = \frac{\tan\left( A + B \right) - \tan\left( A - B \right)}{1 + \tan\left( A + B \right)\tan\left( A - B \right)} \left[ \tan\left( - \theta \right) = - \tan \theta \right]\]

\[ = \frac{x - y}{1 + xy}\]

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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: 21 | Page no. 20
Solution If Tan (A + B) = X and Tan (A − B) = Y, Find the Values of Tan 2a and Tan 2b. Concept: Trigonometric Functions of Sum and Difference of Two Angles.
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