Question

The number of solutions of ${\sin }^{3}x-{\cos }^{4}x=1$ for $x\in [-2\pi ,2\pi ]$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

${\sin }^{3}x-{\cos }^{4}x=1$
$\Rightarrow {\sin }^{3}x=1+{\cos }^{4}x\ge 1$ but ${\sin }^{3}x\le 1$
$\Rightarrow {\sin }^{3}x=1,{\cos }^{4}x=0$
$\Rightarrow \sin x=1,\cos x=0$
Only two possible solutions $\frac{\pi }{2},-\frac{3\pi }{2}$