a-maths~~~~~~~~

2007-10-12 3:04 pm
証明恆等式
sin(750°+θ)tan(765°+θ)tan(225°+θ)sec(θ-60°)=1

回答 (1)

2007-10-12 6:32 pm
✔ 最佳答案
LHS:
sin(750°+θ)tan(765°+θ)tan(225°+θ)sec(θ-60°)
= sin (2 * 360°+ 30°+θ) tan (2 * 360°+45°+θ) tan(270 °-45°+θ) [1/cos(θ-60°)]
= sin (30°+θ) tan(45°+θ) tan(θ-45°) [1/cos(60°-θ)]
= sin (30°+θ) tan(45°+θ) tan(θ-45°) [1/cos(90°-30°-θ)]
= sin (30°+θ) tan(45°+θ) tan(θ-45°) [1/sin (30°+θ)]
= tan(45°+θ) tan(θ-45°)
= [ (tan45°+tanθ)/(1- tan45°tanθ)] * [ (tanθ - tan45°)/(1+ tan45°tanθ)]
= [ (1+tanθ)/(1- tanθ)] * [ (tanθ - 1)/(1+ tanθ)]
= 1
= RHS


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