Question

化简：cos(θ+4π)cos²(θ+π)sin²(θ＋3π)/sin(θ－4π)sin﹙5π+θ﹚cos²﹙－θ－π﹚

Answer 1

cos(θ+4π)cos²(θ+π)sin²(θ＋3π)/sin(θ－4π)sin﹙5π+θ﹚cos²﹙－θ－π﹚
=cosθ(-cosθ)²(-sinθ)²/sinθsin﹙π+θ﹚cos²﹙θ+π﹚
=cosθcos²θsin²θ/sinθ(-sinθ﹚(-cosθ)²
=-cosθcos²θsin²θ/sinθsinθcos²θ
=-cosθcos²θ/cos²θ
=-cosθ

Answer 2

cos(θ+4π)cos²(θ+π)sin²(θ＋3π)/sin(θ－4π)sin﹙5π+θ﹚cos²﹙－θ－π﹚
=cosθ*(-cosθ)²*(-sinθ)²/[sinθ*(-sinθ)*(-cosθ)²]
=cosθ*cos²θ*sin²θ/(-sin²θ*cos²θ)
=-cosθ

Answer 3

cos(θ+4π)cos²(θ+π)sin²(θ＋3π)/sin(θ－4π)sin?5π+θ?cos²?－θ－π?
=cosθ(-cosθ)²(-sinθ)²/sinθsin?π+θ?cos²?θ+π?
=cosθcos²θsin²θ/sinθ(-sinθ?(-cosθ)²
=-cosθcos²θsin²θ/sinθsinθcos²θ
=-cosθcos²θ/cos²θ
=-cosθ cos(θ+4π)cos²(θ+π)sin²(θ＋3π)/sin(θ－4π)sin?5π+θ?cos²?－θ－π?
=cosθ*(-cosθ)²*(-sinθ)²/[sinθ*(-sinθ)*(-cosθ)²]
=cosθ*cos²θ*sin²θ/(-sin²θ*cos²θ)
=-cosθ