Question

If $\cos \alpha =-\frac{12}{13},\cot \beta =\frac{24}{7},{90}^{\circ }$ < $\alpha$ < ${180}^{\circ }$ and ${180}^{\circ }$ < $\beta$ < ${270}^{\circ },$ then the quadrant in which $\alpha +\beta$ lies

• A. I
• B. II
• C. III
• D. IV

Answer 1

The correct option is D IV

${90}^{\circ }$ < $\alpha$ < ${180}^{\circ }$ and ${180}^{\circ }$ < $\beta$ < ${270}^{\circ }\Rightarrow {270}^{\circ }$ < $\alpha +\beta$ < ${450}^{\circ }\Rightarrow \alpha +\beta ϵI\left(or\right)IV$
$Tan(\alpha +\beta )=\frac{\frac{-5}{12}+\frac{7}{24}}{1-\left[\frac{-5}{12}\right].\frac{7}{24}}$ < 0. $\therefore \alpha +\beta ϵIV$