plzzz help me by integrating this troublesome question

Correction : ... cos(a-b) should be cos (x-b).
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... ∫ { 1 / [ cos (x-a). cos (x-b) ] } dx

= [ 1 / sin (a-b) ] · ∫ { sin (a-b) / [ cos (x-a). cos (x-b) ] } dx

= csc (a-b) ∫ { sin [ (x-b) - (x-a) ] } / [ cos (x-a). cos (x-b) ] dx

= csc (a-b) ∫ { sin(x-b). cos(x-a) - cos(x-b). sin(x-a) } / [ cos(x-a). cos(x-b) ] dx ... Now Split

= csc (a-b) ∫ { [ tan (x-b) ] - [ tan (x-a) ] } dx

= csc (a-b) { ln | sec (x-b) | - ln | sec (x-a) | } + C

= csc (a-b) · ln | sec (x-b) / sec (x-a) | + C

= csc (a-b) · ln | cos (x-a) / cos (x-b) | + C ...................... Ans.
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Happy To Help !
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