Question

The roots of the equation ${\cos }^{7}x+{\sin }^{4}x=1$ in the interval $(-\pi ,\pi )$ are

• A. $\{-\frac{\pi }{2},0,\frac{\pi }{2}\}$
• B. $\{-\frac{\pi }{2},\frac{\pi }{2}\}$
• C. $\left\{\frac{\pi }{2}\right\}$
• D. $\left\{\frac{\pi }{4}\right\}$

Answer 1

The correct option is A $\{-\frac{\pi }{2},0,\frac{\pi }{2}\}$

solution can occur only when

${\cos }^{7}x=0,{\sin }^{4}x=1$

or ${\cos }^{7}x=1,{\sin }^{4}x=0$

so,

$x=-\frac{\pi }{2},0,\frac{\pi }{2}$