A) \[45{}^\circ \]
B) \[37.5{}^\circ \]
C) \[32.5{}^\circ \]
D) \[35{}^\circ \]
Correct Answer: B
Solution :
We have, \[\sin (A+B)=\frac{1}{\sqrt{2}}=\sin 45{}^\circ \] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,A+B=45{}^\circ \] .(1) |
and \[\cos (A-B)=\frac{\sqrt{3}}{2}=\cos 30{}^\circ \] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,A-B=30{}^\circ \] ...(2) |
Adding eqs. (1) and (2), we get |
\[(A+B)+(A-B)=45{}^\circ +30{}^\circ \,\,\Rightarrow \,\,\,2A=75{}^\circ \,\,\Rightarrow \,\,A=37.5{}^\circ \] |
So, option [b] is correct. |
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