A) \[\frac{17}{30}\]
B) \[\frac{30}{17}\]
C) \[0\]
D) \[1\]
Correct Answer: C
Solution :
| From part (1), \[\cos R=\frac{8}{17}\] |
| \[\Rightarrow \,\,\,\,\sin R=\sqrt{1-{{\cos }^{2}}R}=\sqrt{1-{{\left( \frac{8}{17} \right)}^{2}}}=\sqrt{1-\frac{64}{289}}=\sqrt{\frac{225}{289}}=\frac{15}{17}\]and from part (2), |
| \[\cos ec\,\,P=\frac{17}{8}\,\,\,\,\Rightarrow \,\sin P=\frac{8}{17}\] |
| \[\therefore \,\,\,\,\,\,\,\cos P=\sqrt{1-{{\sin }^{2}}P}=\sqrt{1-{{\left( \frac{8}{17} \right)}^{2}}}=\frac{15}{17}\] |
| So, \[\frac{\sin R-\cos P}{\sin R+\cos P}=\frac{\left( \frac{15}{17}-\frac{15}{17} \right)}{\left( \frac{15}{17}+\frac{15}{17} \right)}=\frac{0}{(30/17)}=0\] |
| So, option [c] is correct. |
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