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If \( \beta+\cos ^{2} \alpha, \beta+\sin ^{2} \alpha \) are the roots of \( x^{2}+2 b x+c=0 \) and \( \gamma+\cos ^{4} \alpha, \gamma+\sin ^{4} \alpha \) are the roots of
W \( \mathrm{X}^{2}+2 \mathrm{BX}+\mathrm{C}=0 \), then prove that \( \mathrm{b}^{2}-\mathrm{B}^{2}=\mathrm{c}-\mathrm{C} \).
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