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BITSAT 2011

Exam: BITSAT
Year: 2011
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

BITSAT 2011 · Mathematics · Trigonometric Ratios & Identities

If, ( A=(1)/(2) ) and ( B= (1)/(3) ), then find the value of ( A+B )

If, (\tan

\mathrm{A}=\frac{1}{2}

) and (\tan B=

\frac{1}{3}

), then find the value of (

\mathrm{A}+\mathrm{B}

)

Options

A(\pi)
B( $\frac{\pi}{2}$ )
C( $\frac{\pi}{4}$ )
D( $\frac{-\pi}{4}$ )

Correct answer

C. ( $\frac{\pi}{4}$ )

Step-by-step solution

(

\begin{aligned} & \tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2} \cdot \frac{1}{3}}=1 \\ & \therefore A+B=45^{\circ}=\frac{\pi}{4} \end{aligned}

)

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