证明sin^4α-cos^4α=sin^2α-cos^2α我左边分解因式是(sin^2α-cos^2α)(sin^2α+cos^2_数学解答

证明sin^4α-cos^4α=sin^2α-cos^2α
我左边分解因式是(sin^2α-cos^2α)(sin^2α+cos^2α)...怎么看都不相等
是题目错了还是我想错了?

人气：375 ℃　时间：2020-08-28 02:14:24

解答

（sinα）^4-(cosα)^4
=(sin²α)²-(cos²α)²
=(sin²α-cos²α)(sin²α+cos²α)[sin²α+cos²α=1]
=sin²α-cos²α