Answers

2014-08-20T00:02:14+05:30
Formula :
1. (x + y + z)^{2} =  x^{2} +  y^{2} +  z^{2} + 2xy + 2yz + 2zx
2. sin^{2}( \alpha ) +  cos^{2}( \alpha ) = 1
3. sin( \alpha )sin( \beta ) + cos( \alpha )cos( \beta ) = cos( \alpha -  \beta )


A = sin( \frac{2 \pi }{7} ) + sin( \frac{4 \pi }{7} ) + sin( \frac{8 \pi }{7} ) \\  \\  A^{2} =  sin^{2}( \frac{2 \pi }{7} ) + sin^{2}( \frac{4 \pi }{7} ) + sin^{2}( \frac{8 \pi }{7} ) + 2sin( \frac{2 \pi }{7} )sin( \frac{4 \pi }{7} ) + 2sin( \frac{4 \pi }{7} )sin( \frac{8 \pi }{7} ) + 2sin( \frac{8 \pi }{7} )sin( \frac{2 \pi }{7} ) \\  \\B = cos( \frac{2 \pi }{7} ) + cos( \frac{4 \pi }{7} ) + cos( \frac{8 \pi }{7} )

B^{2} = cos^{2}( \frac{2 \pi }{7} ) + cos^{2}( \frac{4 \pi }{7} ) + cos^{2}( \frac{8 \pi }{7} ) + 2cos( \frac{2 \pi }{7} )cos( \frac{4 \pi }{7} ) + 2cos( \frac{4 \pi }{7} )cos( \frac{8 \pi }{7} ) + 2cos( \frac{8 \pi }{7} )cos( \frac{2 \pi }{7} )

So,
 A^{2} +  B^{2} =  (sin^{2}( \frac{2 \pi }{7} ) +  cos^{2}( \frac{2 \pi }{7} )) + (sin^{2}( \frac{4 \pi }{7} ) +  cos^{2}( \frac{4 \pi }{7} )) + (sin^{2}( \frac{8 \pi }{7} ) +  cos^{2}( \frac{8 \pi }{7} )) + 2(sin( \frac{2 \pi }{7} )sin( \frac{4 \pi }{7} ) + cos( \frac{2 \pi }{7} )cos( \frac{4 \pi }{7} )) + 2(sin( \frac{4 \pi }{7} )sin( \frac{8 \pi }{7} ) + cos( \frac{4 \pi }{7} )cos( \frac{8 \pi }{7} )) + 2(sin( \frac{8 \pi }{7} )sin( \frac{2 \pi }{7} ) + cos( \frac{8 \pi }{7} )cos( \frac{2 \pi }{7} ))

A^{2} +  B^{2} = 1 + 1 + 1 + 2cos( \frac{2 \pi }{7} ) + 2cos( \frac{4 \pi }{7} ) + 2cos( \frac{6 \pi }{7} ) \\  \\ A^{2} +  B^{2} = 3 + 2(cos( \frac{2 \pi }{7} ) + cos( \frac{6 \pi }{7} )) + 2cos( \frac{4 \pi }{7} ) \\  \\A^{2} +  B^{2} = 3 + 2(2cos( \frac{4 \pi }{7} )cos( \frac{2 \pi }{7} )) + 2cos( \frac{4 \pi }{7} )

A^{2} +  B^{2} = 3 + 4cos( \frac{4 \pi }{7})cos( \frac{2 \pi }{7} ) + 2cos( \frac{4 \pi }{7} ) \\  \\A^{2} + B^{2} = 3 + 2cos( \frac{4 \pi }{7})(2cos( \frac{2 \pi }{7} ) + 1)\\ \\\sqrt{A^{2} + B^{2}} =\sqrt{3 + 2cos( \frac{4 \pi }{7})(2cos( \frac{2 \pi }{7} ) + 1)}
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seriously .... i thought it's the best solution .....
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whose ans u should the brainliest answer? check out the time who solved first.....
be a little sincere, ..... don't u think, the solution is exact copy of mine....