A) \[0\]
B) \[1\]
C) \[\frac{97}{85}\]
D) \[\frac{589}{986}\]
Correct Answer: D
Solution :
| From part (1), \[\sec S=\frac{\sqrt{34}}{3}\Rightarrow \cos S=\frac{3}{\sqrt{34}}\] |
| \[\therefore \,\,\,\,\sin S=\sqrt{1-{{\cos }^{2}}S}=\sqrt{1-\frac{9}{34}}=\sqrt{\frac{25}{34}}=\frac{5}{\sqrt{34}}\] |
| From part (2), \[\cos ec\,R=\frac{\sqrt{29}}{5}\Rightarrow \sin R=\frac{5}{\sqrt{29}}\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\cos R=\sqrt{1-{{\sin }^{2}}R}=\sqrt{1-\frac{25}{29}}=\sqrt{\frac{4}{29}}=\frac{2}{\sqrt{29}}\] |
| \[\therefore \,\,\,\,\,\,{{\sin }^{2}}S-{{\cos }^{2}}R={{\left( \frac{5}{\sqrt{34}} \right)}^{2}}-{{\left( \frac{2}{\sqrt{29}} \right)}^{2}}=\frac{25}{34}-\frac{4}{29}\] |
| \[=\frac{725-136}{986}=\frac{589}{986}\] |
| So, option [d] is correct. |
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