A) 2 sin \[\alpha \]
B) 4
C) \[4{{\sin }^{2}}\alpha \]
D) \[-\,4{{\sin }^{2}}\alpha \]
Correct Answer: C
Solution :
[c] \[{{\cos }^{-1}}x-{{\cos }^{-1}}\frac{y}{2}=\alpha \] \[\Rightarrow {{\cos }^{-1}}\left( \frac{xy}{2}+\sqrt{(1-{{x}^{2}})\left( 1-\frac{{{y}^{2}}}{4} \right)} \right)=\alpha \] \[\Rightarrow {{\cos }^{-1}}\left( \frac{xy+\sqrt{4-{{y}^{2}}-4{{x}^{2}}+{{x}^{2}}{{y}^{2}}}}{2} \right)=\alpha \] \[\Rightarrow \sqrt{4-{{y}^{2}}-4{{x}^{2}}+{{x}^{2}}{{y}^{2}}}=2\cos \alpha -xy\] \[\Rightarrow 4-{{y}^{2}}-4{{x}^{2}}+{{x}^{2}}{{y}^{2}}=4{{\cos }^{2}}\alpha \] \[+{{x}^{2}}{{y}^{2}}-4xy\cos \alpha \] \[\Rightarrow \]\[4{{x}^{2}}+{{y}^{2}}-4xy\cos \alpha =4{{\sin }^{2}}\alpha \]
You need to login to perform this action.
You will be redirected in
3 sec
