且cosA=4/5,求√2sin(2A+π/4) 怎样化简

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且cosA=4/5,求√2sin(2A+π/4) 怎样化简
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且cosA=4/5,求√2sin(2A+π/4) 怎样化简
且cosA=4/5,求√2sin(2A+π/4) 怎样化简

且cosA=4/5,求√2sin(2A+π/4) 怎样化简
cosA=4/5,那么sinA=3/5或-3/5
sinA=3/5时,
sin2A=2sinAcosA=24/25
cos2A=2cos²A-1=7/25
√2sin(2A+π/4)
=√2(sin2A*√2/2+cos2A*√2/2)
=sin2A+cos2A
=31/25

sinA=-3/5时,
sin2A=-24/25,cos2a=7/25
√2sin(2A+π/4)
=sin2A+cos2A
=-24/25+7/25
=-17/25

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