JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Easy

1 of 1

Analyzing +4 | -1

The number of solutions of

{\sin ^7}x + {\cos ^7}x = 1,\,\,x \in [0,\,4\pi ]

is equal to

View answer and explanation

Correct option: C

Option C (5) is correct because the equation

{\sin ^7}x + {\cos ^7}x = 1

is satisfied only when

\sin x = 0

\cos x = 0

, or

\sin x = 1

\cos x = 1

, leading to 5 solutions in the interval

[0, 4\pi]

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