Question

The number of real roots of the equation ${\cos }^{2}x+{\sin }^{4}x=1$ in the interval $(-\pi ,\pi )$ are

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

${\cos }^{2}x+{\sin }^{4}x=1\Rightarrow {\sin }^{4}x=1-{\cos }^{2}x\Rightarrow {\sin }^{4}x={\sin }^{2}x\Rightarrow {\sin }^{4}x-{\sin }^{2}x=0\Rightarrow {\sin }^{2}x({\sin }^{2}x-1)=0\Rightarrow {\sin }^{2}x(\sin x-1)(\sin x+1)\Rightarrow x=0,\frac{\pi }{2},\frac{3\pi }{2}$

So, number of solution is $3$

Therefore, Answer is $3$