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Find the indefinite integral int1/(cos(...

Find the indefinite integral `int1/(cos(x-a)cos(x-b))dx`.

Text Solution

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Given, `int1/(cos(x-a)-cos(x-b))dx`
=`1/sin(b-a)intsin[(x−a)−(x−b)]/(cos(x-a)-cos(x-b))dx`
=`1/sin(b-a)int[sin(x−a)cos(x-b)−sin(x−b)cos(x-a)]/(cos(x-a)cos(x-b))dx`
=`1/sin(b-a)∫[tan(x−b)−tan(x−a)].dx`
=`1/sin(b-a)log[cos(x−a)/cos(x−b)​]+c`
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