The value of lim x → 0 ⁡ 1 - cos 3 ⁡ x sin 2 ⁡ x cos ⁡ x is equal to

Question

The value of lim x → 0 ⁡ 1 - cos 3 ⁡ x sin 2 ⁡ x cos ⁡ x is equal to,

MARKS App · Accepted Answer

lim x → 0 ⁡ 1 - cos 3 ⁡ x sin 2 ⁡ x cos ⁡ x = lim x → 0 ⁡ 1 - cos ⁡ x 1 + cos 2 ⁡ x + cos ⁡ x sin 2 ⁡ x cos ⁡ x = lim x → 0 ⁡ 2 sin 2 ⁡ x 2 1 + cos 2 ⁡ x + cos ⁡ x 2 sin ⁡ x 2 cos ⁡ x 2 2 cos ⁡ x = lim x → 0 1 2 ⋅ 1 + cos 2 x + cos x cos x 2 2 cos x = 1 2 3 1 = 3 2

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