sin cos 小問題2個^^

問題(1)
1/sinX = cosec X
1/cosX =sec X

問題(2) 其他常用的三角恆等式: 〔θ及 ψ是某角〕
I) Trigomometric Relations
sec²θ = 1+ tan²θ
cosec²θ= 1+ cot²θ

II)Half Angle Formula
sin(θ/2) = ±√[(1 - cosθ)/2]
cos(θ/2) =± √[(1 + cosθ)/2]
tan(θ/2) = ±√[(1 - cosθ)/(1 + cosθ)] = (1 - cosθ)/sinθ = sinθ/(1 - cosθ)
If t = tan(θ/2), then
sinθ = 2t/(1 + t²)
cosθ = (1 - t²)/(1 + t²)
tanθ = - 2t/(1 - t²)

III) Compound Angle Formula
sin(θ+ ψ) = sinθcosψ + cosθsinψ
sin(θ- ψ) = sinθcosψ - cosθsinψ
cos(θ+ ψ) = cosθcosψ- sinθsinψ
cos(θ- ψ) = cosθcosψ+ sinθsinψ
tan(θ+ ψ) = (tanθ+ tanψ)/(1 - tanθtanψ)
tan(θ- ψ) = (tanθ- tanψ)/(1 + tanθtanψ)

IV)Multiple Angle Formula
sin2θ = 2 sinθcosθ
cos2θ= cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2 sin²θ
tan2θ = 2tanθ/(1 - tan²θ)
sin3θ = 3sinθ - 4sin 3 θ
cos3θ = 4cos 3 θ - 3cosθ
tan3θ = (3tanθ- tan 3 θ)/(1 - 3 tan²θ)

V) Product-to-Sum Formula
sinθcosψ = 1/2[ sin(θ+ ψ) + sin(θ- ψ)]
cosθsinψ = 1/2[ sin(θ+ ψ) - sin(θ- ψ)]
cosθcosψ = 1/2[ cos(θ+ ψ) + cos(θ- ψ)]
sinθsinψ = 1/2[ cos(θ+ ψ) - cos(θ- ψ)]

VI) Sum-to-Product Formula
sinθ+ sinψ = 2sin[(θ+ ψ)/2]cos[(θ- ψ)/2]
sinθ- sinψ = 2cos[(θ+ ψ)/2]sin[(θ- ψ)/2]
cosθ+ cosψ = 2cos[(θ+ ψ)/2]cos[(θ- ψ)/2]
cosθ- cosψ = - 2sin[(θ+ ψ)/2]sin[(θ- ψ)/2]

(1) 其實1/sin x 或1/cos x都冇特別意思的
1/sin x = cosec x
1/cos x= sec x

(2) 仲有好多ge...不過都係a math出現
好似sec^2 x = tan^2 x + 1
csc^2 x = cot^2 x +1
sin 2x = 2sin x cos x
cos 2x = cos^2 x - sin^2 x
tan 2x = 2tan x / 1- tan^2 x

其實仲有好多條－．－”
希望幫到你啦