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Evaluate int(1)/(cos(x-a)cos(x-b))dx...

Evaluate
`int(1)/(cos(x-a)cos(x-b))dx`

Text Solution

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` int (1)/(cos (x-a) cos (x-b)) dx`
` =(1)/(sin (a-b) )int (sin (a-b))/(cos(x-a)cos (x-b))dx`
`=(1)/(sin (a-b))int (sin{(x-b)-(x-a)}}/(cos (x -b)cos (x-b))dx`
` =(1)/(sin(a-b)) int (-sin (x-a) cos (x-b))/(cos(x-a) cos (x-b))dx`
`=(1)/(sin(a-b))int {tan(x-b) -tan (x-a) }dx`
` =(1)/(sin(a-b))l-lgo |cos (x-b)|`
` +log |cos (x-a)|]+c`
` =(1)/(sin (a-b)) log |(cos (x-a))/(cos(x-b))| +c`
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