lim x → π 2 cot x - cos x π - 2 x 3 equals

Step-by-step solution

Put, x = π 2 - h in the given limit, we get = lim h → 0 cot π 2 - h - cos π 2 - h π - 2 × π 2 - h 3 = lim h → 0 tan h - sin h π - 2 × π 2 + 2 h 3 = lim h → 0 tan h - sin h 8 h 3 =   1 8   lim h → 0 sin h h sec h - 1 h 2 = 1 8   lim h → 0 sin h h lim h → 0 1 - cos h cos h   h 2 = 1 8   × 1 × lim h → 0 1 - cos h cos h   h 2 = 1 8   lim h → 0 2 sin 2 h 2 cos h   h 2 = 1 8 &#160