Question

Number of solutions of equation ${\sin }^{65}x-{\cos }^{65}x=-1$ in the interval $(-\pi ,\pi )$ is __

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

$si{n}^{65}x-co{s}^{65}x=-1$

The above $e{q}^n$ holds true if sin x = -1 or cos x = 1

sin x = -1 if $x=+3\pi /2$, $-\pi /2\Rightarrow x=-\pi /2$ $[\because +\frac{3\pi }{2}]$

cos x = 1 when $x=0\in (-\pi /\pi )$

$\Rightarrow x=-\pi /2$ or $x=0$

Thus, there are 2 solutions.