A) \[2\sin 2\alpha \]
B) \[4\]
C) \[4{{\sin }^{2}}\alpha \]
D) \[-4{{\sin }^{2}}\alpha \]
Correct Answer: C
Solution :
[c] \[{{\cos }^{-1}}x-{{\cos }^{-1}}\frac{y}{2}=\alpha \] \[{{\cos }^{-1}}\left( \frac{xy}{2}+\sqrt{(1-{{x}^{2}})\left( 1-\frac{{{y}^{2}}}{4} \right)} \right)=\alpha \] \[\Rightarrow 4-{{y}^{2}}-4{{x}^{2}}+{{x}^{2}}{{y}^{2}}\] \[=4{{\cos }^{2}}\alpha +{{x}^{2}}{{y}^{2}}-4xy\cos \alpha \] \[\Rightarrow 4{{x}^{2}}+{{y}^{2}}-4xy\cos \alpha =4{{\sin }^{2}}\alpha .\]
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