Question

Lim tanx .sin^2 4x / (sin4x-2sin2x)
⁡(x→0)

Answer 1

Lim { tanx.sin 4x. sin 4x } / { 2 sin 2x cos 2x - 2 sin2x}
Lim { tanx.sin 4x. sin 4x } / { 2 sin 2x (cos2x - 1) }
Lim { (tanx.sin4x.sin4x) } / { 2sin2x(-2sin^2  x) }
Lim {tanx.sin4x.sin4x} / { 2sin2x(-2) sinx. sinx}

(1/2) . (1/2) . (-1/2) .(4/1) . (4/1)
= -2