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求证sin^2x+sin^2y-sin^2x*sin^2y+cos^2x*cos^2y=1
题目详情
求证sin^2x+sin^2y-sin^2x*sin^2y+cos^2x*cos^2y=1
▼优质解答
答案和解析
sin^2x+sin^2y-sin^2x*sin^2y+cos^2x*cos^2y
= sin^2x-sin^2x*sin^2y+sin^2y+cos^2x*cos^2y
= sin^2x*(1-sin^2y)+sin^2y+cos^2x*cos^2y
= sin^2x*cos^2y+sin^2y+cos^2x*cos^2y
= sin^2x*cos^2y+cos^2x*cos^2y+sin^2y
= cos^2y(sin^2x+cos^2x)+sin^2y
= cos^2y *1 + sin^2y
= cos^2y + sin^2y
= 1
= sin^2x-sin^2x*sin^2y+sin^2y+cos^2x*cos^2y
= sin^2x*(1-sin^2y)+sin^2y+cos^2x*cos^2y
= sin^2x*cos^2y+sin^2y+cos^2x*cos^2y
= sin^2x*cos^2y+cos^2x*cos^2y+sin^2y
= cos^2y(sin^2x+cos^2x)+sin^2y
= cos^2y *1 + sin^2y
= cos^2y + sin^2y
= 1
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