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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of lim x → 0 ⁡ 1 - cos 4 ⁡ x 5 sin 2 ⁡ x cos ⁡ x is equal to

Correct answer

0.4

Step-by-step solution

lim x → 0 ⁡ 1 - cos 4 ⁡ x 5 sin 2 ⁡ x cos ⁡ x = lim x → 0 ⁡ 1 - cos ⁡ x 1 + cos 3 ⁡ x + cos 2 ⁡ x + cos ⁡ x 5 sin 2 ⁡ x cos ⁡ x = lim x → 0 ⁡ 2 sin 2 ⁡ x 2 1 + cos ⁡ x + cos 2 ⁡ x + cos 3 ⁡ x 2 sin ⁡ x 2 cos ⁡ x 2 2 5 cos ⁡ x = lim x → 0 1 2 ⋅ 1 + cos x + cos 2 x + cos 3 x cos x 2 2 5 cos x = 2 5

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