A) \[0\]
B) \[1\]
C) \[\frac{97}{85}\]
D) \[\frac{589}{986}\]
Correct Answer: D
Solution :
From part (1). \[\sec S=\frac{\sqrt{34}}{3}\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\cos S=\frac{3}{\sqrt{34}}\] |
From part (2). \[\cos ec\,R=\frac{\sqrt{29}}{5}\Rightarrow \sin R=\frac{5}{\sqrt{29}}\] |
\[\therefore \,\,\,{{\sin }^{2}}R-{{\cos }^{2}}S={{\left( \frac{5}{\sqrt{29}} \right)}^{2}}-{{\left( \frac{3}{\sqrt{34}} \right)}^{2}}=\frac{25}{29}-\frac{9}{34}\] |
\[=\frac{850-261}{986}=\frac{589}{986}\] |
So, option [d] is correct. |
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