三角函数求解：若tanx=1/2,求sin^2x+2sinxsin(π/2-x)+3sin^2(3π/2-x)

三角函数求解：若tanx=1/2,求sin^2x+2sinxsin(π/2-x)+3sin^2(3π/2-x)
三角函数求解：若tanx=1/2,求sin^2x+2sinxsin(π/2-x)+3sin^2(3π/2-x)

三角函数求解：若tanx=1/2,求sin^2x+2sinxsin(π/2-x)+3sin^2(3π/2-x)
sin^2x+2sinxsin(π/2-x)+3sin^2(3π/2-x)
=sin²x+2sinxcosx+3sin²(π/2-x)
=sin²x+sin2x+3cos²x
=1+2cos²x+sin2x
tanx=1/2
所以
|sinx|=√5/5
|cosx|=2√5/5
所以
上式=1+2×(4/5)+2×(√5/5)×(2√5/5)
=1+8/5+4/5
=17/5