The value of lim x → π ⁡ tan ⁡ π cos 2 ⁡ x sin 2 ⁡ 2 x is equal to

Step-by-step solution

Let, x = π + t lim t → 0 ⁡ tan ⁡ π cos 2 ⁡ π + t sin 2 ⁡ 2 π + 2 t = lim t → 0 ⁡ tan ⁡ π cos 2 ⁡ t sin 2 ⁡ 2 t = lim t → 0 ⁡ tan ⁡ π - π sin 2 ⁡ t sin 2 ⁡ 2 t = lim t → 0 ⁡ - tan ⁡ π sin 2 ⁡ t 4 π sin 2 ⁡ t cos 2 ⁡ t · π = - π 4