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Evaluate: lim_x→0 [(tan x - sin x) / (sin³ x)]

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lim_x→0 [(tanx - sin x) / (sin³ x)] = lim_x→0 [(sinx (1/cosx - 1)) / (sin³ x)]

= lim_x→0 [(1 - cosx) / (cosx × sin² x)]

= lim_x→0 [(2sin²(x/2)) / (cosx × 4sin²(x/2) cos²(x/2))]

= lim_x→0 [1 / (2 cos x × cos²(x/2))]

= 1/2

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Evaluate: limx→0 [(tan x - sin x) / (sin3 x)]

Verified Answer

Evaluate: limx→0 [(tan x - sin x) / (sin3 x)]

Verified Answer

Evaluate: lim_x→0 [(tan x - sin x) / (sin³ x)]

Evaluate: lim_x→0 [(tan x - sin x) / (sin³ x)]