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Find the number of real solution of the equation `(cos x)^(5)+(sin x)^(3)=1` in the interval `[0, 2pi]`

Text Solution

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The correct Answer is:
Three solutions
`cos^(5) x le cos^(2) x and sin^(3) x le sin^(2) x`
So, `cos^(5)x+sin^(3) x=1` is possible only when `cos^(5) x= cos^(2) x` and `sin^(3) x= sin^(2) x`, which is possible only at `x=0, pi//2, and 2pi`.
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