证明:sin²α+sin²β-sin²αsin²β+cos²αcos&
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/13 14:21:36
证明:sin²α+sin²β-sin²αsin²β+cos²αcos²β=1
![证明:sin²α+sin²β-sin²αsin²β+cos²αcos&](/uploads/image/z/16763122-10-2.jpg?t=%E8%AF%81%E6%98%8E%EF%BC%9Asin%26%23178%3B%CE%B1%2Bsin%26%23178%3B%CE%B2-sin%26%23178%3B%CE%B1sin%26%23178%3B%CE%B2%2Bcos%26%23178%3B%CE%B1cos%26)
sin²α+sin²β-sin²αsin²β+cos²αcos²β
=sin²α(1-sin²β)+sin²β+cos²αcos²β
=sin²αcos²β+sin²β+cos²αcos²β
=(sin²α+cos²α)cos²β+sin²β
=cos²β+sin²β
=1
=sin²α(1-sin²β)+sin²β+cos²αcos²β
=sin²αcos²β+sin²β+cos²αcos²β
=(sin²α+cos²α)cos²β+sin²β
=cos²β+sin²β
=1
sin²α+sin²β—sin²αsin²β+cos²αcos
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