If tanA-12 and tanB-13 then A-B -

The correct option is B 3π/4 #160;tan A= 1 2 and #160;tan B= 1 3 Now #160; #160;tan( A+B ) #160; =tan A +tan B #160; 1 tan ...

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Standard XII

Mathematics

Integration by Partial Fractions

If tanA=-12...

Question

If $tan A = - \frac{1}{2}$ and $tan B = - \frac{1}{3}$ then $A + B =$

\frac{π}{4}

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\frac{3 π}{4}

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\frac{5 π}{4}

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None

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Solution

The correct option is B $\frac{3 π}{4}$
$tan A = - \frac{1}{2}$ and $tan B = - \frac{1}{3}$
Now
$tan (A + B) = \frac{tan A + tan B}{1 - tan A tan B}$
$= \frac{- \frac{1}{2} - \frac{1}{3}}{1 - (- \frac{1}{2}) (- \frac{1}{3})} = \frac{- \frac{5}{6}}{1 - \frac{1}{6}} = \frac{- \frac{5}{6}}{- \frac{5}{6}} = - 1$
$\Rightarrow A + B = {tan}^{- 1} (- 1) = \frac{3 π}{4}$

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