Question

Integrate: cos(x-a) / cos(x+a)​

Answer 1

Answer:

x cos(2a)+ ln|sec(x+a)|+C

Step-by-step explanation:

Hope this will help you...!

Answer 2

Answer:

(x+a)cos2a + sin2a x log[sec(x+a)] + c

Step-by-step explanation:

$\int\limits \, cos(x-a)/cos(x+a) dx$  (1)

here let x+a=t   (2)

             x=t-a    (3)

      differntiate w.r.t  t , we get

            dx/dt=1-0

therefore,  dx=dt  (4)

Put  (2), (3) ,(4) in equation (1) we get

   $\int\limits \,cos(t-a-a)/cost dx$

$\int\limits \, cos(t-2a)/cost dx$

$\int\limits \,cost*cos2a+sint*sin2a/cost dx$   [cos(a+b)=cos a*cos b+sin a*sin b]

$\int\limits \,(cost*cos2a/cost ) + (sint*sin2a/cost) dx$

$\int\limits \,cos2a + tant*sin2a dx$    (tant=sint/cost)

$cos2a\int\limits \,1 dx +sin2a\int\limits \,tant dx$   (since 'a' is a constant)

cos2a(t)+sin2a*log(sect)+c

Re substitution of 't' we get,

(x+a)cos2a + sin2a x log[sec(x+a)] + c

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