A) \[2n\pi +\frac{\pi }{2}\]
B) \[2n\pi +\frac{\pi }{3}\]
C) \[n\pi +\frac{\pi }{2}\]
D) \[n\pi +\frac{\pi }{3}\]
Correct Answer: B
Solution :
We have, \[{{\sin }^{50}}x-{{\cos }^{50}}x=1\Rightarrow {{\sin }^{50}}x=1+{{\cos }^{50}}x\] Since \[{{\sin }^{50}}x\le 1\] and \[1+{{\cos }^{50}}x\ge 1\]. therefore, the two sides are equal only if \[{{\sin }^{50}}x=1=1+{{\cos }^{50}}x\] i.e \[{{\sin }^{50}}x=1\] and \[{{\cos }^{50}}x=0\] \[\therefore \,\,\,x=2n\pi +\frac{\pi }{2},\,\,n\in I\].
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