The value of lim x → 2 π ⁡ cos ⁡ x - cos ⁡ x cos ⁡ x 1 - cos ⁡ x + ln ⁡ cos ⁡ x is equal to

Question

The value of lim x → 2 π ⁡ cos ⁡ x - cos ⁡ x cos ⁡ x 1 - cos ⁡ x + ln ⁡ cos ⁡ x is equal to,

MARKS App · Accepted Answer

Let, L = l i m x → 2 π cos ⁡ x - ( cos ⁡ x ) cos ⁡ x 1 - cos ⁡ x + ln ⁡ cos ⁡ x Putting cos ⁡ x = t , we get, L = lim t → 1 ⁡ t - t t 1 - t + ln ⁡ t Now by L-Hospital rule L = l i m t → 1 1 - t t ( 1 + ln ⁡ t ) - 1 + 1 t Again by L-Hospital rule = l i m t → 1 - t t 1 t - t t 1 + ln ⁡ t 2 - 1 t 2 = 2

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