the tangents of two acute angles are 3 and 2.The sine of twice their difference is

A)7/24

B)7/48

C)7/50

D)7/25

As slope of acute angle are 3 and 2 respectively.
So tanθ = 3 and tan ϕ= 2
Hence the difference of angles are tan-1(3) - tan-1(2) =tan-1(3-21+6) =tan-1(17)Let tan-117 = yHence tany =17 , hence siny =150So   tan-117 = sin-1150So sin(sin-1150) =150 (ans) This answer is closest to 7/50 .

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