NIMCET 2012 — Mathematics PYQ

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Question

NIMCET 2012 — Mathematics PYQ

NIMCET | Mathematics | 2012

If $A - B = \frac{\pi}{4}$ , then $(1 + \tan A)(1 - \tan B)$ is equal to:

Choose the correct answer:

Explanation

Step 1: Use the tangent subtraction formula

Given $A - B = \frac{\pi}{4}$ . Taking $\tan$ on both sides:

\tan(A - B) = \tan\left(\frac{\pi}{4}\right)

\frac{\tan A - \tan B}{1 + \tan A \tan B} = 1

Step 2: Rearrange the equation

\tan A - \tan B = 1 + \tan A \tan B

\tan A - \tan B - \tan A \tan B = 1

Step 3: Evaluate the required expression

Expand the given expression:

(1 + \tan A)(1 - \tan B) = 1 - \tan B + \tan A - \tan A \tan B

Rearranging the terms:

1 + (\tan A - \tan B - \tan A \tan B)

Step 4: Substitute the value from Step 2

From Step 2, we know that $(\tan A - \tan B - \tan A \tan B) = 1$ .

(1 + \tan A)(1 - \tan B) = 1 + 1 = 2

Correct Option: (a)

Choose the correct answer:

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