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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

ConceptTrigonometric Functions of Sum and Difference of Two Angles

#### 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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