Question

Plzz solve this easy calculus :')

Answer 1

`\sin \: x - \cos x \: + c`

Explanation:

`\int (cos2x)/( √(1 - sin2x) ) dx \\ \\ = \int \frac{ {cos}^(2)x - {sin}^(2)x } { \sqrt{ {sin}^(2)x + {cos}^(2)x - 2sinx \: cosx } } dx \\ \\ = \int \frac{ ({cos}x - {sin}x )({cos}x + {sin}x )} { \sqrt{ {({cos}x - {sin}x )}^(2) } } dx \\ \\ = \int \frac{ ({cos}x - {sin}x )({cos}x + {sin}x )} {{ {({cos}x - {sin}x )} } } dx \\ \\ = \int({cos}x + {sin}x)dx \\ \\ = \int{cos}x \: dx + \int{sin}x \: dx \\ \\ = \sin \: x - \cos x \: + c`