CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The value of $$\cos{\displaystyle\frac{\pi}{7}}\cos{\displaystyle\frac{2\pi}{7}}\cos{\displaystyle\frac{3\pi}{7}}$$ is


A
0
loader
B
12
loader
C
13
loader
D
18
loader

Solution

The correct option is D $$\displaystyle\frac{1}{8}$$
The value of $$\displaystyle \cos { \frac { \pi  }{ 7 }  } \cos { \frac { 2\pi  }{ 7 }  } \cos { \frac { 3\pi  }{ 7 }  } $$
$$\displaystyle =\frac { 2\sin { \frac { \pi  }{ 7 }  } \cos { \frac { \pi  }{ 7 }  } \cos { \frac { 2\pi  }{ 7 }  } \cos { \frac { 3\pi  }{ 7 }  }  }{ 2\sin { \frac { \pi  }{ 7 }  }  } $$
$$\displaystyle =\frac { \sin { \frac { 2\pi  }{ 7 }  } \cos { \frac { 2\pi  }{ 7 }  } \cos { \frac { 3\pi  }{ 7 }  }  }{ 2\sin { \frac { \pi  }{ 7 }  }  } $$
$$\displaystyle =\frac { \sin { \frac { 4\pi  }{ 7 }  } \cos { \frac { 3\pi  }{ 7 }  }  }{ 4\sin { \frac { \pi  }{ 7 }  }  } =\frac { \sin { \frac { 3\pi  }{ 7 }  } \cos { \frac { 3\pi  }{ 7 }  }  }{ 4\sin { \frac { \pi  }{ 7 }  }  } $$
$$\displaystyle =\frac { \sin { \frac { 6\pi  }{ 7 }  }  }{ 8\sin { \frac { \pi  }{ 7 }  }  } =\frac { \sin { \left( \pi -\frac { \pi  }{ 7 }  \right)  }  }{ 8\sin { \frac { \pi  }{ 7 }  }  } =\frac { \sin { \frac { \pi  }{ 7 }  }  }{ 8\sin { \frac { \pi  }{ 7 }  }  } =\frac { 1 }{ 8 } $$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image