Total number of solutions of${\sin ^4}x + {\cos ^4}x = \sin x\,\, \cdot \,\,\cos x\,\;{\rm{in}}\,\;\left[ {0,\;\,2\pi } \right]$ is equal to

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Total number of solutions of

{\sin ^4}x + {\cos ^4}x = \sin x\,\, \cdot \,\,\cos x\,\;\mathrm{in}\,\;\left[ {0,\;\,2\pi } \right]

is equal to

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Correct option: A

Option A (2) is correct because by simplifying the given equation, we find that there are only two solutions for x in the interval [0, 2

\pi

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