# If Tan (A + B) = P and Tan (A − B) = Q, Then Write the Value of Tan 2b. - Mathematics

Short Note

If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B

#### Solution

$\tan 2B = \tan(B + B)$
$= \tan(A + B - (A - B))$
$= \frac{\tan(A + B) - \tan(A - B)}{1 + \tan(A + B)\tan(A - B)}$
$= \frac{p - q}{1 + pq} \left[ \because \tan(A + B) = p \text{ and } \tan(A - B) = q \right]$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 7 Values of Trigonometric function at sum or difference of angles
Q 7 | Page 27