`int(cos2x-cos2theta)/(cosx-costheta)\ dx` is equal to `2\ (sinx+xcostheta)+C` (b) `2\ (sinx-xcostheta)+C` (c) `2\ (sinx+2xcostheta)+C` (d) `2\ (sinx-2xcostheta)+C`

Explanation

`I=∫(cos2x−cos2θ​)/(cosx−cosθ)dx`

`=∫(cos^2x−1−2cos^2θ+1)/(cosx−cosθ)​dx`

`=∫(2(cos^2x−cos^2θ))/(cosx−cosθ)​dx`

`=2∫((cosx−cosθ)(cosx+cosθ)​)/(cosx−cosθ)dx`

`=2∫(cosx+cosθ)dx`

`=2(sinx+xcosθ)+C `