If $$\sin \theta - \cos \theta = \frac{7}{{13}}$$ and $${0^ \circ }{\text{ < }}\theta {\text{ < }}{90^ \circ }{\text{,}}$$ then the value of $$\sin \theta $$ + $${\text{cos}}\theta $$ is?
A. $$\frac{{17}}{{13}}$$
B. $$\frac{{13}}{{17}}$$
C. $$\frac{1}{{13}}$$
D. $$\frac{1}{{17}}$$
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & \sin \theta - \cos \theta = \frac{7}{{13}} = \alpha \cr & {\text{When, }} \cr & ax + by = m\,......(i) \cr & bx - ay = n\,......(ii) \cr} $$By adding these two equations after making square on both sides we get,
$$\eqalign{ & \left( {{a^2} + {b^2}} \right)\left( {{x^2} + {y^2}} \right) = {m^2} + {n^2} \cr & {\text{In the same process}} \cr & \sin \theta \pm \cos \theta = a \cr & {\text{Then,}}\sin \theta \pm \cos \theta = \sqrt {2 - {a^2}} \cr & \Rightarrow \sin \theta + \cos \theta = \sqrt {2 - {{\left( {\frac{7}{{13}}} \right)}^2}} \cr & \Rightarrow \sin \theta + \cos \theta = \sqrt {2 - \left( {\frac{{49}}{{169}}} \right)} \cr & \Rightarrow \sin \theta + \cos \theta = \sqrt {\frac{{289}}{{169}}} \cr & \Rightarrow \sin \theta + \cos \theta = \frac{{17}}{{13}} \cr} $$
Related Questions on Trigonometry
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B. x > y
C. x = y
D. x < y
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