If-tan-2-atan-2-b-tan-2-btan-2-c-tan-2-ctan-2-a-2tan-2-atan-2-btan-2-c-1-then-find-the-value-of-sin-2-a-sin-2-b-sin-2-c-

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Question Number 29131 by $@ty@m last updated on 04/Feb/18

If tan^2 atan^2 b+tan^2 btan^2 c+tan^2 ctan^2 a +2tan^2 atan^2 btan^2 c=1 then find the value of: sin^2 a+sin^2 b+sin^2 c

$${If}\:\mathrm{tan}^{\mathrm{2}} {a}\mathrm{tan}\:^{\mathrm{2}} {b}+\mathrm{tan}^{\mathrm{2}} {b}\mathrm{tan}\:^{\mathrm{2}} {c}+\mathrm{tan}^{\mathrm{2}} {c}\mathrm{tan}\:^{\mathrm{2}} {a} \\ $$$$+\mathrm{2tan}^{\mathrm{2}} {a}\mathrm{tan}^{\mathrm{2}} {b}\mathrm{tan}\:^{\mathrm{2}} {c}=\mathrm{1} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}: \\ $$$$\mathrm{sin}\:^{\mathrm{2}} {a}+\mathrm{sin}\:^{\mathrm{2}} {b}+\mathrm{sin}\:^{\mathrm{2}} {c} \\ $$

Commented by $@ty@m last updated on 13/Feb/18