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Number of roots of the equation (3+cos"x...

Number of roots of the equation `(3+cos"x")^2=4-2sin^8x ,x in [0,5pi]a r e` _________

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LHS
`-1<=cosx<=1`
`2<=3+cosx<=4`
`4<=(3+cosx)^2<=16`
`4<=LHS<=16`
RHS
`-1<=sinx<1`
`0<=sin^8x<=1`
...
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