Question

$\int \frac{cos(x-a)}{cos(x-b)}dx$

• A. $xcos(b-a)-sin(b-a)log|sec(x-b)|+c$
• B. $xcos(b-a)+sin(b-a)log|sec(x-b)|+c$
• C. $xcos(b+a)-sin(b+a)log|sec(x+b)|+c$
• D. $xcos(b+a)+sin(b+a)log|sec(x-b)|+c$

Answer 1

Answer: (A)

$xcos(b-a)-sin(b-a)log|sec(x-b)|+c$

$\frac{\cos (x-a)}{\cos (x-b)}=\frac{\cos (x-b+(b-a\left)\right)}{\cos (x-b)}=\cos (b-a)-\tan (x-b)\sin (b-a)$

$\int \frac{\cos (x-a)}{\cos (x-b)}dx=\cos (b-a)\int dx-\sin (b-a)\int \tan (x-b)dx=x\cos (b-a)-\sin (b-a)\log |\text{sec}(x-b)|+C$