Sin²β+Sin²α+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:2024/06/24 08:45:18
Sin²β+Sin²α+Sin²αSin²β+Cos²αCos²β 等于多少?
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![Sin²β+Sin²α+Sin²αSin²β+Cos²αCos](/uploads/image/z/16093530-18-0.jpg?t=Sin%26%23178%3B%CE%B2%2BSin%26%23178%3B%CE%B1%2BSin%26%23178%3B%CE%B1Sin%26%23178%3B%CE%B2%2BCos%26%23178%3B%CE%B1Cos%26%2317)
因为Cos²αCos²β=(1-Sin²α)*(1-Sin²β)=1-Sin²β-Sin²α+Sin²αSin²β
所以Sin²β+Sin²α+Sin²αSin²β+Cos²αCos²β
=Sin²β+Sin²α+Sin²αSin²β+(1-Sin²β-Sin²α+Sin²αSin²β)
=1+2Sin²αSin²β
因此,你确定题目没写错?
所以Sin²β+Sin²α+Sin²αSin²β+Cos²αCos²β
=Sin²β+Sin²α+Sin²αSin²β+(1-Sin²β-Sin²α+Sin²αSin²β)
=1+2Sin²αSin²β
因此,你确定题目没写错?
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