If CosA=-3/5, SinB=725 and 90°<A<180°, 0°<B<90° then Tan A+B=

cos A=-35, 3sin B=725tan A=-43 tan B=724tan(A+B)=tan A+tan B1-tan A tan B =-43+7241+43 724 =-96+2172+28 =-75100 =-34

If CosA=-3/5, SinB=725 and 90°<A<180°, 0°<B<90° then Tan A+B=

cos A=-35, 3sin B=725tan A=-43 tan B=724tan(A+B)=tan A+tan B1-tan A tan B =-43+7241+43 724 =-96+2172+28 =-75100 =-34

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If $CosA = - 3 / 5, SinB = \frac{7}{25}$ and $90 ° < A < 180 °, 0 ° < B < 90 °$ then $Tan (A + B) =$

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$\frac{3}{5}$

$\frac{3}{4}$

$- \frac{3}{4}$

$- \frac{3}{5}$

answer is B.

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Detailed Solution

$\begin{array}{rcl} \cos A & = & \frac{- 3}{5}, 3 \sin B = \frac{7}{25} \\ \tan A & = & \frac{- 4}{3} \tan B = \frac{7}{24} \\ \tan (A + B) & = & \frac{\tan A + \tan B}{1 - \tan A \tan B} \\ = & \frac{\frac{- 4}{3} + \frac{7}{24}}{1 + \frac{4}{3} \frac{7}{24}} \\ = & \frac{- 96 + 21}{72 + 28} \\ = & \frac{- 75}{100} \\ = & \frac{- 3}{4} \end{array}$