Trigonometric EquationHard
Question
In ᐃABC, which of the following is/are possible (where notations have usual meaning)
Options
A.sin A : sin B : sin C = 1 : 2 : 3
B.ᐃ = 
C.(a + b + c)(a + b - c) = 3ab
D.b2 - c2 = aR
Solution
(A) a : b : c = 1 : 2 : 3
(B) ᐃ =
bc sin A = 
sin A =
(possible)
(C) (a + b)2 - c2 = 3ab
a2 + b2 - c2 = ab
cos C =
(possible)
(D) 4R2(sin2B - sin2C) = 2R2sin A
sin (B + C) sin (B - C) =
sin A
sin(B - C) =
(possible)
(B) ᐃ =
bc sin A = sin A =
(possible)(C) (a + b)2 - c2 = 3ab
a2 + b2 - c2 = ab
cos C =
(possible)(D) 4R2(sin2B - sin2C) = 2R2sin A
sin (B + C) sin (B - C) =
sin Asin(B - C) =
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