Using the measurements given in the following figure, the value of + - is . . . . . . . .

Using the measurements given in the following figure, the value of $$\frac{\sin \varphi +\tan \theta }{\sin \varphi -\tan \theta }$$   is . . . . . . . .

Answer: Option A

Solution

Answer: Option A

Solution:

$$\begin{array}{rl}& \Rightarrow \frac{\sin \varphi +\tan \theta }{\sin \varphi -\tan \theta }\\ & =\frac{\frac{5}{13}+\frac{12}{9}}{\frac{5}{13}-\frac{12}{9}}\\ & =\frac{15+52}{39}\times \frac{39}{15-52}\\ & =-\frac{67}{37}\end{array}$$