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\[QR=a\] \[\therefore \]\[PR=\sqrt{{{a}^{2}}+\frac{{{a}^{2}}}{4}}=\frac{\sqrt{5a}}{2}\] \[\therefore \]\[1:\alpha :\beta =\frac{a}{2}:a:\frac{\sqrt{5a}}{2}=1:2:\sqrt{5}\] \[\therefore \]\[\alpha =2\]\[\beta =\sqrt{5}\] \[\therefore \]\[{{\alpha }^{2}}+{{\beta }^{2}}=9\]You need to login to perform this action.
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