Trigonometric EquationHard

Question

In triangle ABC, 2ac sin (A - B + C) =

Options

A.a2 + b2 - c2
B.c2 - a2 - b2
C.b2 - a2 - c2
D.c2 - a2 - b2

Solution

We know that, A + B + C = 180o
⇒     A + C - B = 180 - 2B
Now, 2ac sin = 2ac sin(90o - B)
= 2ac cos B = = a2 + c2 - b2

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