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Integrate the functions1/(cos(x+a)cos(x+...

Integrate the functions`1/(cos(x+a)cos(x+b)`

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`int(1)/(cos(x+a)cos(x+b))dx=I " (say) "`
`:. I=(1)/(sin(a-b)) int(sin(a-b))/(cos(x+a)cos(x+b))dx`
` I= (1)/(sin (a-b)) int(sin[(x+a)-(x+b)])/(cos(x+a)cos (x+b))dx`
`sin (x+a)cos(c+b)`
`=(1)/(sin(a-b)) int(-cos (x+a)sin(x+b))/(cos(x+a)cos (x+b))dx`
`=(1)/(sin(a-b)) int[(sin(x+a))/(cos(x+a))-(sin(x+b))/(cos(x+b))]dx`
` =(1)/(sin (a-b))int[tan (x+a)-tan (x+b)]dx`
`+log |cos (x+b)|"]"+C`
`=(1)/(sin(a-b))log |(cos (x+b))/(cos(x+a))|+C`
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