Question

Total number of solutions of $sin^4x +cos^4x = sin x cos x$ is $[0,2\pi]$ is equal to

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (A)

2

Answer 2

$sin^4 \,x + cos^4 \,x = sin \,x \,cos\,x$
$\Rightarrow (sin^2\,x + cos^2 \,x)^2 - 2\,sin^2\,x \cdot cos^2\,x = sin\,x \cdot cos\,x$
$\Rightarrow 1- \frac{ sin^2 \,2x}{2} = \frac{sin\,2x}{2}$
$\Rightarrow sin^2\, 2x + sin\,2x - 2 = 0$
$\Rightarrow ( sin \,2x + 2) ( sin \,2x - 1) = 0$
$\Rightarrow sin \,2x = 1$
$\Rightarrow 2x = (4n + 1) \frac{\pi}{2}$
$\Rightarrow x = (4n + 1) \frac{\pi}{4}$
$\Rightarrow x =\frac{\pi}{4}, \frac{5\pi}{4}$