Question

A trignometry question

Answer 1

\[\cos 3\pi/14+\cos 5\pi/14+\cos7\pi/14+\cos9\pi/14+\cos11\pi/14\]

Answer 2

please solve the above question for meee

Answer 3

Lets simplify this problem a little using these facts:
\[\cos(\frac{11\pi}{14}) = \cos(\pi -\frac{3\pi}{14}) = -\cos(\frac{3\pi}{14})\]
\[\cos(\frac{9\pi}{14}) = \cos(\pi -\frac{5\pi}{14}) = -\cos(\frac{5\pi}{14})\]

Answer 4

Thus the addition becomes:\[\cos3π/14+\cos5π/14+\cos7π/14-\cos5π/14-\cos3π/14 \]
\[\cos(\frac{\pi}{2}) = 0\]

Answer 5

if there is any confusion let me know :)

Answer 6

how it will be \[\cos \pi/2?\] can u explain alittle i understood others Thank you so much

Answer 7

the only term that does cancel out is the:
\[\cos(\frac{7\pi}{14})\]
but:
\[\frac{7}{14} \Rightarrow \frac{1}{2}\]
it reduces. So we really have:
\[\cos(\frac{\pi}{2})\]

Answer 8

sry, "...that doesnt* cancel...."

Answer 9

you r really genius in trignometry thank you dear sirrr!!!