Question #a9666

Question

3140 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-18T16:09:01

$LHS=Cos (pi/11 )cos ((2pi)/11 )cos ((3pi)/11 )cos ((4pi)/11 )cos ((5pi)/11 )$

$=1/(16sin(pi/11))*8*2sin(pi/11)Cos (pi/11 )cos ((2pi)/11 )cos ((4pi)/11 )cos ((3pi)/11 )cos ((5pi)/11 )$

$=1/(16sin(pi/11))*4*2sin((2pi)/11)cos ((2pi)/11 )cos ((4pi)/11 )cos ((3pi)/11 )cos ((5pi)/11 )$

$=1/(16sin(pi/11))*2*2sin((4pi)/11)cos ((4pi)/11 )cos (pi-(8pi)/11 )cos ((5pi)/11 )$

$=1/(16sin(pi/11))*2sin((8pi)/11)cos (pi-(8pi)/11 )cos ((5pi)/11 )$

$=-1/(32sin(pi/11))*2sin((16pi)/11)cos ((5pi)/11 )$

$=-1/(32sin(pi/11))*2sin(pi+(5pi)/11)cos ((5pi)/11 )$

$=1/(32sin(pi/11))*2sin((5pi)/11)cos ((5pi)/11 )$

$=1/(32sin(pi/11))*sin((10pi)/11)$

$=1/(32sin(pi/11))*sin(pi-pi/11)$

$=1/(32sin(pi/11))*sin(pi/11)$

$=1/32=RHS$

Proved