Properties of Triangle

In a ∆ABC, if `sin"A"/sin"C" = (sin("A" - "B"))/(sin("B" - "C"))` prove that a², b², C² are in Arithmetic Progression

The angles of a triangle ABC, are in Arithmetic Progression and if b : c = `sqrt(3) : sqrt(2)`, find ∠A

In a ∆ABC, if cos C = `sin "A"/(2sin"B")` show that the triangle is isosceles

In an ∆ABC, prove that a cos A + b cos B + c cos C = 2a sin B sin C

In a ∆ABC, prove that `sin "B"/sin "C" = ("c" - "a"cos "B")/("b" - "a" cos"C")`

In a ∆ABC, ∠A = 60°. Prove that b + c = `2"a" cos (("B" - "C")/2)`

In an ∆ABC, prove the following, `"a"sin ("A"/2 + "B") = ("b" + "c") sin  "A"/2`

In a ∆ABC, prove the following, a(cos B + cos C) = `2("b" + "c") sin^2  "A"/2`