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Originally posted in a technical section, so missing the template

**Mod note: Fixed the LaTeX.**

##a=sinθ+sinϕ##

##b=tanθ+tanϕ##

##c=secθ+secϕ##

Show that,

##8bc=a[4b^2 + (b^2-c^2)^2]##

I tried to solve this for hours and have gotten no-where. Here's what I've got so far :

##a= 2\sin(\frac{\theta+\phi}{2})\cos(\frac{\theta-\phi}{2}) ##

## b = \frac{2\sin(\theta+\phi)}{\cos(\theta+\phi)+\cos(\theta-\phi)}##

##c=\frac{2(\cos\theta+\cos\phi)}{\cos(\theta+\phi)+\cos(\theta-\phi)}##

##a^2 = \frac{\sin^2(\theta+\phi)[\cos(\theta+\phi)+1]}{\cos(\theta+\phi)+1}##

##\\cos(\theta-\phi)=\frac{ca}{b}-1##

##sin^2(\frac{\theta+\phi}{2})=\frac{2a^2b}{4(ca+b)}##

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