A) 1
B) 2
C) ½
D) None of these
Correct Answer: B
Solution :
[b] \[{{\sin }^{-1}}x+{{\sin }^{-1}}y=\frac{\pi }{2}\Rightarrow {{\sin }^{-1}}x=\frac{\pi }{2}-{{\sin }^{-1}}y\] \[\Rightarrow {{\sin }^{-1}}x={{\sin }^{-1}}\sqrt{1-{{y}^{2}}}\Rightarrow {{x}^{2}}+{{y}^{2}}=1\] \[\Rightarrow \frac{1+{{x}^{4}}+{{y}^{4}}}{{{x}^{2}}-{{x}^{2}}{{y}^{2}}+{{y}^{2}}}=\frac{1+{{({{x}^{2}}+{{y}^{2}})}^{2}}-2{{x}^{2}}{{y}^{2}}}{1-{{x}^{2}}{{y}^{2}}}\] \[=\frac{1+1-2{{x}^{2}}{{y}^{2}}}{1-{{x}^{2}}{{y}^{2}}}=2.\]
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