A) \[{{60}^{o}},\text{ }{{30}^{o}}\]
B) \[{{75}^{o}},\text{ }{{15}^{o}}\]
C) \[{{45}^{o}},\text{ }{{60}^{o}}\]
D) \[{{45}^{o}},\text{ }{{45}^{o}}\]
Correct Answer: A
Solution :
\[\sin (A+B)=1\] and\[\cos (A-B)=\frac{\sqrt{3}}{2}\] \[\Rightarrow \] \[A+B=\frac{\pi }{2}\] and \[A-B=\frac{\pi }{6}\] \[\Rightarrow \] \[A=\frac{\pi }{3},\,B=\frac{\pi }{6}\].
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