যদি ${\displaystyle A+B=\frac{\pi }{4}}$ হয়,তবে ( ${\displaystyle (\tan A+1)(\tan B+1)}$এর মান কোনটি?

দেওয়া আছে, \(A + B = \frac{\pi}{4}\)

আমরা জানি, \(tan(A + B) = \frac{tanA + tanB}{1 - tanA \cdot tanB}\)

সুতরাং, \(tan(\frac{\pi}{4}) = \frac{tanA + tanB}{1 - tanA \cdot tanB}\)

যেহেতু, \(tan(\frac{\pi}{4}) = 1\)

অতএব, \(1 = \frac{tanA + tanB}{1 - tanA \cdot tanB}\)

\(=> 1 - tanA \cdot tanB = tanA + tanB\)

\(=> 1 = tanA + tanB + tanA \cdot tanB\)

এখন, \((tanA + 1)(tanB + 1) = tanA \cdot tanB + tanA + tanB + 1\)

\(= (tanA + tanB + tanA \cdot tanB) + 1\)

\(= 1 + 1\)

\(= 2\)

অতএব, \((tanA + 1)(tanB + 1) = 2\)