A) \[9\]
B) \[8\]
C) \[6\]
D) \[7\]
Correct Answer: A
Solution :
\[2\sec 4C+{{\sin }^{2}}2A+\sqrt{\sin B}=0\] \[A={{45}^{o}},\,\,B={{90}^{o}}\]and\[C={{45}^{o}}\] Let\[AQ=a\], then\[BP=\frac{a}{2}\], \[PQ=\frac{a}{2}\]and\[QR=a\] \[\therefore \]\[PR=\sqrt{{{a}^{2}}+\frac{{{a}^{2}}}{4}}=\frac{\sqrt{5}a}{2}\] \[\therefore \]\[1:\alpha :\beta =\frac{a}{2}:a:\frac{\sqrt{5}a}{2}=1:2:\sqrt{5}\] \[\therefore \]\[\alpha =2\]and\[\beta =\sqrt{5}\]\[\therefore \]\[{{\alpha }^{2}}+{{\beta }^{2}}=9\]You need to login to perform this action.
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