Question Number 9211 by tawakalitu last updated on 23/Nov/16
![If sinA + sinB = a tanA + tanB = b secA + secB = c Prove that, 8bc = a[4b^2 + (b^2 − c^2 )]^2](https://www.tinkutara.com/question/Q9211.png)
$$\mathrm{If} \\ $$$$\mathrm{sinA}\:+\:\mathrm{sinB}\:=\:\mathrm{a} \\ $$$$\mathrm{tanA}\:+\:\mathrm{tanB}\:=\:\mathrm{b} \\ $$$$\mathrm{secA}\:+\:\mathrm{secB}\:=\:\mathrm{c} \\ $$$$\mathrm{Prove}\:\mathrm{that}, \\ $$$$\mathrm{8bc}\:=\:\mathrm{a}\left[\mathrm{4b}^{\mathrm{2}} \:+\:\left(\mathrm{b}^{\mathrm{2}} \:−\:\mathrm{c}^{\mathrm{2}} \right)\right]^{\mathrm{2}} \\ $$