Question

The number of $x \in [0, 2 \pi]$ for which $| \sqrt{2 \sin^4 x + 18 \cos^2 x} - \sqrt{2 \cos^4 x + 18\sin^2 x}| = 1$ is :

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (D)

$\sqrt{2\,sin^{4}\,x+18\,cos^{2}\,x}-\sqrt{2\,cos^{4}\,x+18\,sin^{2}\,x}=1$
$\sqrt{2\,sin^{4}\,x+18\,cos^{2}\,x}-\sqrt{2\,cos^{4}\,x+18\,sin^{2}\,x}=\pm1$
$\sqrt{2\,sin^{4}\,x+18\,cos^{2}\,x}=\pm1+\sqrt{2\,cos^{4}\,x+18\,sin^{2}\,x}$
by squaring both the sides we will get B solutions