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求证:
\({\sin^{4}}\alpha -{\cos^{4}}\alpha =2{\sin^{2}}\alpha -1\)
参考答案:左边\( = ({\sin ^2}\alpha - {\cos ^2}\alpha )({\sin ^2}\alpha + {\cos ^2}\alpha ) = {\sin ^2}\alpha - {\cos ^2}\alpha = {\sin ^2}\alpha - (1 - {\sin ^2}\alpha ) = 2{\sin ^2}\alpha - 1 = \) 右边
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