A) 1
B) -1
C) 0
D) 2
Correct Answer: A
Solution :
[a] Let, \[{{\sin }^{-1}}x={{\tan }^{-1}}y=\theta \] \[\Rightarrow x=\sin \theta \] and \[y=\tan \theta \] \[\frac{1}{{{x}^{2}}}=\frac{1}{{{\sin }^{2}}\theta }=\cos e{{c}^{2}}\theta \] And \[\frac{1}{{{y}^{2}}}=\frac{1}{{{\tan }^{2}}\theta }={{\cot }^{2}}\theta .\] \[\Rightarrow \frac{1}{{{x}^{2}}}-\frac{1}{{{y}^{2}}}=\cos e{{c}^{2}}\theta -{{\cot }^{2}}\theta =1\]
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