中四數學題

圖片參考：https://s.yimg.com/lo/api/res/1.2/ZQit8r6YM3UMER1bF6V.OQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://i.imgur.com/ZH9B85L.gif

1.
sin(270° - θ) / sin(θ) + cos(90° + θ) / cos(θ)
= sin(180° + 90° - θ) / sin(θ) + cos[180° - (90° - θ)] / cos(θ)
= -sin(90° - θ) / sin(θ) - cos(90° - θ) / cos(θ)
= -cos(θ) / sin(θ) - sin(θ) / cos(θ)
= -[ cos(θ) / sin(θ) + sin(θ) / cos(θ) ]
= -{ [cos²(θ) + sin²(θ)] / [sin(θ) cos(θ)] }
= -1/[sin(θ) cos(θ)]

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2.
4sin(90° - θ) × sin(θ - 360°) + cos(270° - θ)
= 4cos(θ) × [-sin(360° - θ)] + cos(180° + 90° - θ)
= -4cos(θ) × sin(360° - θ) - cos(90° - θ)
= -4cos(θ) × [-sin(θ)] - sin(θ)
= 4sin(θ)cos(θ) - sin(θ)
= sin(θ)[4cos(θ) - 1]

1.
sin(270 ° - θ ) / sin θ + cos(90 °+ θ ) / cos θ
=-cos θ /sin θ -sin θ /cos θ
=-[(1/tan θ )+tan θ ]
=-[1+(tan θ )(tan θ )]/tan θ

2.
4sin(90 °- θ ) * sin(θ-360°) + cos (270°-θ )
=4cos θ sin θ -sin θ
=sin θ (4cos θ -1)