Chứng mình

Cos pi/11+cos 3pi/11+cos 5pi/11+cos 7pi/11+cos 9pi/11=1/2

Ai giúp cho mình câu này với

`cos\ pi/11+cos\ (3pi)/11+cos\ (5pi)/11+cos\ (7pi)/11+cos\ (9pi)/11=1/2`

`=>VT. sin\ \pi/11=sin\ pi/11.(cos\ pi/11+cos\ (3pi)/11+cos\ (5pi)/11+cos\ (7pi)/11+cos\ (9pi)/11)`

`=sin\ pi/11. cos\ pi/11+sin\ pi/11. cos\ (3pi)/11+sin\ pi/11. cos\ (5pi)/11+sin\ pi/11.cos\ (7pi)/11+sin\ pi/11. cos\ (9pi)/11`

`=1/2. sin\ (2pi)/11+1/2.[sin\ (4pi)/11+sin\ (-2pi)/11]+1/2.[sin\ (6pi)/11+sin\ (-4pi)/11]+1/2.[sin\ (8pi)/11+sin\ (-6pi)/11]+1/2.[sin\ (10pi)/11+sin\ (-8pi)/11]`

`=1/2.(sin\ (2pi)/11+sin\ (4pi)/11+sin\ (-2pi)/11+sin\ (6pi)/11+sin\ (-4pi)/11+sin\ (8pi)/11+sin\ (-6pi)/11+sin\ (10pi)/11+sin\ (-8pi)/11)`

 `=1/2.[(sin\ (2pi)/11+sin\ (-2pi)/11)+(sin\ (4pi)/11+sin\ (-4pi)/11)+(sin\ (6pi)/11+sin\ (-6pi)/11)+(sin\ (8pi)/11+sin\ (-8pi)/11)+sin\ (10pi)/11]`

`=1/2.(0+0+0+0+sin\ (10pi)/11)`

`=1/2. sin\ (10pi)/11`

`=>`$VT=\dfrac{\dfrac{1}{2}.\sin \dfrac{10\pi}{11}}{\sin \dfrac{\pi}{11}}=\dfrac{1}{2}=VP\ (\text{điều phải chứng minh})$