Question

sin(B-C)/cosB ×cosC=tanB-tanC​

Answer 1

Answer:

Left hand side = sin(B-C) / cos(B) × cos(C)

We know that

Sin( α - β ) = Sin(α)cos(β) - sin(β)cos(α)

And

Tan(Ф) = Sin(Ф) / Cos(Ф)

So

Sin( α - β ) = ( Sin(B)cos(C) - sin(C)cos(B) ) / cos(B) × cos(C)

                 = Sin(B)cos(C) / cos(B) × cos(C) - sin(C)cos(B) / cos(B) × cos(C)

                 = Sin(B) / Cos(B) - Sin(C) / Cos(C)

                 = Tan(B) - Tan(C) = Right hand side

Hence prove

L.H.S = R.H.S