The number of solutions of sin^7 x + cos^7 x = 1 x ∈ [0, 4π], is equal to

Question

Accepted Answer

Correct answer: C. (c) sin^7 x ≤ sin^2 x ≤ 1...(1) and cos^7 x ≤ cos^2 x ≤ 1 ….(2) also sin^2 x + cos^2 x = 1 ⇒equality must hold for (1)&(2)⇒ sin^7 x = sin^2 x&cos^7 x= cos^2 x ⇒ sin x = 0&cos x = 1 or cos x = 0&sin x = 1 ⇒x=0,2 π,4 π, π2, 5 π2 ⇒ 5 solutions

$The number of solutions of s i n^{7} x + co s^{7} x = 1 x \in [0, 4π], is equal to$

Solution

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