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Ierofanga [76]
2 years ago
9

Plzz solve this easy calculus :')

Mathematics
1 answer:
Digiron [165]2 years ago
3 0

Answer:

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

Step-by-step explanation:

\int \frac{cos2x}{ \sqrt{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

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