Show that cos-cos-sin-sin-2

cosθ #160; +cosϕ #160; #160; sinθ #160; +sinϕ #160; #160; = 2sin( θ +ϕ #160; 2 #160; ) #160; cos( θ ϕ #160; 2 #160; ) #16 ...

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Algebraic Identities

Show that co...

Question

Show that $\frac{cos θ + cos ϕ}{sin θ + sin ϕ} = cot (\frac{θ + ϕ}{2})$

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Solution

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\frac{cos θ + cos ϕ}{sin θ + sin ϕ} = cot (\frac{θ + ϕ}{2})

sin θ + sin ϕ = a

cos θ + cos ϕ = b

{tan}^{2} (\frac{θ - ϕ}{2})

a = cos θ + i sin θ, b = cos ϕ + i sin ϕ, c = cos ψ + i sin ψ

\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = 2

sin (θ - ϕ) + sin (ϕ - ψ) + sin (ψ - θ)

c o s θ, s i n θ)

(c o s ϕ, s i n ϕ)

θ a n d ϕ

s i n (\frac{θ - ϕ}{2}) = \pm \frac{1}{\sqrt{2}}

c o s (\frac{θ - ϕ}{2}) = \pm \frac{1}{\sqrt{2}}

sin θ

sin ϕ

cos ϕ

cos 2 θ = 2 {cos}^{2} (\frac{π}{4} + ϕ)

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