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What is the Integration of 1/[(cos(x-a)cos(x-b)] dx

What is the Integration of 1/[(cos(x-a)cos(x-b)] dx

Grade:12

2 Answers

Suraj Singh
148 Points
5 years ago
In these questions.. Remember a rule to multiply and divide by sin(a-b) if both the trigonometric function is same ie sin n sin or cos n cos... If they are different then multiply and divide by cos(a-b)... And apply trigonometric formulae to get ur integration
moumi roy
91 Points
5 years ago
∫{1/[(cos(x-a)cos(x-b)] } dx
(1/sin(a-b)}∫{sin[(x-a)-(x-b)]}/[(cos(x-a)cos(x-b)]} dx
(1/sin(a-b)}∫{sin(x-a)*cos(x-b)-sin(x-b)*cos(x-a)}/[(cos(x-a)cos(x-b)]dx
(1/sin(a-b)}∫{sin(x-a)/(cos(x-a)-sin(x-b)/cos(x-b)}dx
(1/sin(a-b)}∫{tan(x-a)-tan(x-b)}dx
(1/sin(a-b)}[-ln |cos (x-a)| + -ln |cos (x-b)| ]+ C

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