If tan A - -1-2 and tan B - - 1-3- then A - B - -IIT 1967- MNR 1987- MP PET 1989-

We have tan A = 1/2 and tan B = 1/3 Now, tan(A + B) = tan A + tan B/1 tan A tan B = 1/2 1/3/1 1/2. 1/3 = 1 ⇒ tan(A + B) = tan 3π/4. ...

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Byju's Answer

Standard XI

Mathematics

Trigonometric Ratios for Sum of Two Angles

If tan A = -1...

Question

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

[IIT 1967; MNR 1987; MP PET 1989]

$\frac{π}{4}$

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$\frac{3 π}{4}$

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$\frac{5 π}{4}$

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None of these

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Solution

The correct option is B
$\frac{3 π}{4}$

We have tan A = - $\frac{1}{2}$ and tan B = - $\frac{1}{3}$

Now, tan(A + B) = $\frac{t a n A + t a n B}{1 - t a n A t a n B}$ = $\frac{- \frac{1}{2} - \frac{1}{3}}{1 - \frac{1}{2} . \frac{1}{3}}$ = -1

$\Rightarrow$ tan(A + B) = tan $\frac{3 π}{4}$ . Hence, A + B = $\frac{3 π}{4}$ .

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