已知cosB = cos θsinA,cosC = sinθsinA.θ为已知角.则sin^2 A + sin^2 B +sin^2C等于多少?

来源：学生作业帮助网编辑：作业帮时间：2024/05/03 21:53:48

已知cosB = cos θ*sinA,cosC = sinθ*sinA.θ为已知角.则sin^2 A + sin^2 B +sin^2C等于多少?
已知cosB = cos θ*sinA,cosC = sinθ*sinA.θ为已知角.则sin^2 A + sin^2 B +sin^2C等于多少?

已知cosB = cos θ*sinA,cosC = sinθ*sinA.θ为已知角.则sin^2 A + sin^2 B +sin^2C等于多少?
已知cosB = cos θ*sinA, cosC = sinθ*sinA
所以cosθ=cosB/sinA, sinθ=cosC/SinA
因为（sinθ）^2+(cosθ)^2
=（cosB/sinA）^2+(cosC/SinA)
=(cos^2 B+cos^2 C)/sin^2 A
=1
所以sin^2 A=cos^2 B+cos^2 C
所以sin^2 A + sin^2 B +sin^2 C
=cos^2 B+cos^2 C+ sin^2 B +sin^2 C
=1+1
=2

cosB = cos θ*sinA, cosC = sinθ*sinA
两边同时平方然后相加可得到
cos^2B+cos^2C=sin^2A
整理可得sin^2A+sin^2B +sin^2C=2

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