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Evaluate : (i) int tan^(2)x dx , (ii) i...

Evaluate : (i) `int tan^(2)x dx` , (ii) `intcot^(2)xdx` , (iii) `intsin^(2)x dx`

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(i) `inttan^(2)xdx = int(sec^(2)x - 1) dx`
`= intsec^(2)xdx - intdx = tan x -x + C`.
(ii) `intcot^(2)dx = int(cosec^(2)x - 1)dx`
`= intcosec^(2)xdx - intdx= - cot x - x + C`.
(iii) We know that `2sin^(2)'x/2 = (1-cosx)`.
`because int sin^(2)' x/2dx = 1/2 (1-cosx) dx`
`= 1/2[intdx - int cos x dx] = 1/2 x - 1/2 sin x + C`.
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