Question

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

• A. $\cos a\log \mid \cos (x-a)\mid +c$
• B. $x\sin a+\cos a\log \mid \cos (x-a)\mid +c$
• C. $x\cos a+\sin a\log \mid \cos (x-a)\mid +c$
• D. $(x-a)\sin a+\sin a\log \mid \cos (x-a)\mid +c$

Answer 1

The correct option is C $x\cos a+\sin a\log \mid \cos (x-a)\mid +c$

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

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

$\int \frac{cos\left(\right(x-a)+a)}{\cos (x-a)}dx$

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

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

$\cos a\int 1dx-\sin a\int \tan (x-a)dx$

$\cos a.x-\sin a\log \mid \sec (x-a)\mid +c$