If - = 713 and 0^ < < 90^ , then the value of + cos is?

Answer: Option A

$$\begin{array}{rl}& \sin \theta -\cos \theta =\frac{7}{13}=\alpha \\ & \text{When, }\\ & ax+by=m......(i)\\ & bx-ay=n......(ii)\end{array}$$
By adding these two equations after making square on both sides we get,
$$\begin{array}{rl}& \left(a^2+b^2\right)\left(x^2+y^2\right)=m^2+n^2\\ & \text{In the same process}\\ & \sin \theta \pm \cos \theta =a\\ & \text{Then,}\sin \theta \pm \cos \theta =\sqrt{2-a^2}\\ & \Rightarrow \sin \theta +\cos \theta =\sqrt{2-{\left(\frac{7}{13}\right)}^2}\\ & \Rightarrow \sin \theta +\cos \theta =\sqrt{2-\left(\frac{49}{169}\right)}\\ & \Rightarrow \sin \theta +\cos \theta =\sqrt{\frac{289}{169}}\\ & \Rightarrow \sin \theta +\cos \theta =\frac{17}{13}\end{array}$$