Question

The general solution of the equation ${\sin }^{50}x-{\cos }^{50}x=1$ is-

• A. $2n\pi +\frac{\pi }{2},n\in I$
• B. $2n\pi +\frac{\pi }{3},n\in I$
• C. $n\pi +\frac{\pi }{2},n\in I$
• D. $n\pi +\frac{\pi }{3},n\in I$

Answer 1

Answer: (C)

As ${\sin }^{50}x$ and ${\cos }^{50}x$ are both non-negative
clearly ${\sin }^{50}x=1$ and ${\cos }^{50}x=0$
$\Rightarrow \sin x=\pm 1,\cos x=0$
$\Rightarrow x=n\pi +\frac{\pi }{2}$