A) \[n\pi +\frac{\pi }{4}\]
B) \[2n\pi +\frac{\pi }{4}\]
C) \[2n\pi -\frac{\pi }{4}\]
D) \[\frac{n\pi }{2}+{{(-1)}^{n}}\frac{\pi }{2}\]
Correct Answer: A
Solution :
\[\frac{3\sin (A-{{15}^{o}})}{\cos (A-{{15}^{o}})}=\frac{\sin (A+{{15}^{o}})}{\cos (A+{{15}^{o}})}\] Þ\[3\sin (A-{{15}^{o}})\cos (A+{{15}^{o}})\]\[=\cos (A-{{15}^{o}})\sin (A+{{15}^{o}})\] \[\Rightarrow \] \[2\sin (A-{{15}^{o}})\cos (A+{{15}^{o}})=\frac{1}{2}\] \[\Rightarrow \] \[\sin 2A-\sin {{30}^{o}}=\frac{1}{2}\] \[\Rightarrow \]\[2A=2n\pi +\frac{\pi }{2}\] \[\Rightarrow \] \[A=n\pi +\frac{\pi }{4}\].
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