`lim_(x-pi/2) (cot x - cosx)/(pi-2x)` equals: (1) `1/8` (2) `1/4` (3) `1/24` (4) `1/16`

Explanation

Let `x = pi/2 - h`,

Then, our limit becomes,

`Lim_(h->0) (cot(pi/2-h) - cos(pi/2-h))/(pi -(2(pi/2-h))^3 )`

`=Lim_(h->0) (tanh - sinh)/(pi -2(pi/2-h))^3 `

`=Lim_(h->0) (sinh(1-cosh)/(cosh))/(8h^3) `

`=Lim_(h->0) (tanh(2sin^2(h/2)))/(8h^3) `

`=Lim_(h->0) (tanh(sin^2(h/2)))/(4h^3) `

`=Lim_(h->0) (tanh/h)(sin^2(h/2))/(4*4(h/2)^2) `

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