if-the-sides-a-b-c-of-a-triangle-ABC-are-in-A-P-and-if-sin-A-sin-B-sin-C-cos-sin-B-sin-C-sin-A-cos-sin-C-sin-A-sin-B-cos-then-find-the-value-of-tan-2-2-tan-2-2-

Tinku Tara June 4, 2023 Trigonometry 0 Comments

Question Number 146877 by gsk2684 last updated on 16/Jul/21

if the sides a,b,c of a triangle ABC are in A.P. and if sin A =(sin B +sin C)cos α sin B =(sin C+sin A)cos β sin C =(sin A +sin B)cos γ then find the value of tan^2 (α/2)+tan^2 (γ/2)

$${if}\:{the}\:{sides}\:{a},{b},{c}\:{of}\:{a}\:{triangle}\:{ABC} \\ $$$${are}\:{in}\:{A}.{P}.\:{and}\:{if}\: \\ $$$$\mathrm{sin}\:{A}\:=\left(\mathrm{sin}\:{B}\:+\mathrm{sin}\:{C}\right)\mathrm{cos}\:\alpha \\ $$$$\mathrm{sin}\:{B}\:=\left(\mathrm{sin}\:{C}+\mathrm{sin}\:{A}\right)\mathrm{cos}\:\beta \\ $$$$\mathrm{sin}\:{C}\:=\left(\mathrm{sin}\:{A}\:+\mathrm{sin}\:{B}\right)\mathrm{cos}\:\gamma \\ $$$${then}\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\mathrm{tan}\:^{\mathrm{2}} \frac{\alpha}{\mathrm{2}}+\mathrm{tan}\:^{\mathrm{2}} \frac{\gamma}{\mathrm{2}} \\ $$

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if-the-sides-a-b-c-of-a-triangle-ABC-are-in-A-P-and-if-sin-A-sin-B-sin-C-cos-sin-B-sin-C-sin-A-cos-sin-C-sin-A-sin-B-cos-then-find-the-value-of-tan-2-2-tan-2-2-

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