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2 problems match “counting roots”. Clear

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1. Roots in [0,1] after sine substitution ●●●●○ 100 ptsUsing a suitable substitution, determine the number of roots of the equation $8x(1-2x^2)(8x^4-8x^2+1)=1$ that lie in the interval $[0,1]$.
2. Real roots of a sine-power equation ●●●●○ 100 ptsFind the number of real roots of the equation $\sin(2013\pi x)=x^{2013}$.