Упростите: sin(arccosx-arcsiny)=

Question

Упростите: sin(arccosx-arcsiny)=

Answer 1

task/29453779-_3652

Упростите: sin(arccosx-arcsiny)

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sin(arccosx-arcsiny) =sin(arccosx)*cos(arcsiny) - cos(arccosx)*sin(arcsiny) =

= sin(arcsin√(1-cos²x) )*cos(arccos(√(1-cos²y)) - xy =√(1-cos²x)*√(1-cos²y) - x*y.  || √(1-cos²x)(1-cos²y) - xy ||

Answer 2

sin(arccosx-arcsiny) = sin(arccosx)cos(arcsiny) - sin(arcsiny)cos(arccosx) =

= sin(arccosx)cos(arcsiny) - yx = √(1 - cos²(arccosx))(1 - sin²(arcsiny)) - yx =

= √((1 - x²)(1 - y²)) - yx.