y=sinxcosx=√2(√2/2sinx+√2/2cosx)怎麼变√2sin(x+派/4)?2y=sinxcosx=√2(√2/2sinx+√2/2cosx)怎麼变√2sin(x+派/4)?2(cos2x-1)^2怎麼化2(-2sin^2x)^2?y=sin2x+2cos^2x-1=sin2x+cos2x怎麼化√2sin(2x+派/4)y=sin^2+√3sinxcosx+2cosx^2怎

Question

y=sinxcosx=√2(√2/2sinx+√2/2cosx)怎麼变√2sin(x+派/4)?2
y=sinxcosx=√2(√2/2sinx+√2/2cosx)怎麼变√2sin(x+派/4)?
2(cos2x-1)^2怎麼化2(-2sin^2x)^2?
y=sin2x+2cos^2x-1=sin2x+cos2x怎麼化√2sin(2x+派/4)
y=sin^2+√3sinxcosx+2cosx^2怎麼化?
我不会怎麼合一变换,有什麽方法?
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Answer 1

y=sinx+cosx
=√2(√2/2sinx+√2/2cosx)
=√2(sinxcos派/4+cosxsin派/4)
=√2sin(x+派/4)
∵1-cos2x=2sin^2x
∴2(cos2x-1)^2
=2(-2sin^2x)^2
=8(sinx)^4
∵cos2x= 2cos^2x-1
∴y=sin2x+2cos^2x-1
=sin2x+cos2x
=√2(√2/2sin2x+√2/2cos2x)
=√2(sin2xcos派/4+cos2xsin派/4)
=√2sin(2x+派/4)
y=sin^2+√3sinxcosx+2cosx^2
=sin^2+cosx^2+cosx^2+√3sinxcosx
=1+cosx^2+√3sinxcosx
=1+1/2(1+cos2x)+√3/2sin2x
=3/2+sin2xcos派/6+cos2xsin派/6
=3/2+sin(2x+派/6)