Math, asked by Phoenix007, 1 year ago

find the value of (1+cos π/9)(1+cos3π/9)(1+cos5π/9)(1+cos7π/9)

Answers

Answered by Deepsbhargav
28

 =  > (1 + cos \frac{\pi}{9} )(1 + cos \frac{3\pi}{9} ) \\ (1 + cos \frac{5\pi}{9} )(1 + cos \frac{7\pi}{9} ) \\  \\  =  > (2 {cos}^{2}  \frac{\pi}{18} )(2 {cos}^{2}  \frac{3\pi}{18} ) \\ (2 {cos}^{2}  \frac{5\pi}{18} )(2 {cos}^{2}  \frac{7\pi}{18} ) \\  \\  =  >  {(4sin \frac{4\pi}{9}  \times sin \frac{3\pi}{9} \times sin \frac{2\pi}{9} \times sin \frac{\pi}{9}   )}^{2}
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Now if you see :-

 =  > 4sin \frac{\pi}{9}  \times sin( \frac{\pi}{9}  +  \frac{\pi}{3} ) \times sin( \frac{\pi}{3}  -  \frac{\pi}{9} ) \\  \\  =  > sin(3 \times  \frac{\pi}{9} )
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Hence the given expression :-

  =  > {(sin \frac{3\pi}{9} \times sin \frac{3\pi}{9}  )}^{2}  \\  \\  =  >  {( \frac{3}{4} ) }^{2}  \\  \\  =  >  \frac{9}{16}
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Deepsbhargav: theku ji xD
Deepsbhargav: haan ji
Answered by gnanendraturpati2005
7

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Hey!This may be helpful to you

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