Question

❤ integration of cosec x

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Answer 1

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Answer 2

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I=integ. of cosec x.dx

Multiplying by (cosec x-cot x) in Nr and Dr.

I=integ. of cosec x.(cosec x- cot x).dx/(cosec x-cot x).

Let cosec x- cot x = t

(-cosec x.cot x +cosec^2x ).dx = Dt

cosec x.(-cot x+ cosec x).dx= dt

l=integ. of 1/t.dt

For second form:-

I = log | 1/sin x - cos x /sin x | + C

l== log |(1-cos x)/sin x | +C.

I= log |(1–1+2sin^2 x/2)/(2.sin x/2.cos x/2)| +C.

I= log |(2sin^2 x/2)/(2.sin x/2.cos x/2) | +C.

I= log |sin x/2/cos x/2| + C.

I= log | tan x/2 | + C…………………….(2). Answer