sin (π/n) + sin (3π/n) + sin (5π/n) + .... upto n terms is equal to

Question

sin (π/n) + sin (3π/n) + sin (5π/n) + .... upto n terms is equal to (A) 1 (B) 2 (C) 3 (D) 0

Tardigrade Admin · Accepted Answer

sin (π/n)+ sin (3 π/n)+ sin (5 π/n)+... upto n terms =( sin (n ⋅ 2 π/2 n)/ sin (2 π)2 n) ⋅ sin ((2 ⋅ (π/n)+(n-1) 2 (π/n)/2)) =( sin π/ sin (π)n) ⋅ sin ((2 π+2 n π-2 π/2 n)) =( sin 2 π/ sin (π)n)=0

Q. $sin \frac{π}{n} + sin \frac{3 π}{n} + sin \frac{5 π}{n} + ....$ upto $n$ terms is equal to

$1$

$2$

$3$

$0$

Q. sinnπ​+sinn3π​+sinn5π​+.... upto n terms is equal to

1

2

3

0

sinnπ​+sinn3π​+sinn5π​+... upto n terms =sin2n2π​sin2nn⋅2π​​⋅sin(22⋅nπ​+(n−1)2nπ​​) =sinnπ​sinπ​⋅sin(2n2π+2nπ−2π​) =sinnπ​sin2π​=0

Q. $sin \frac{π}{n} + sin \frac{3 π}{n} + sin \frac{5 π}{n} + ....$ upto $n$ terms is equal to

$1$

$2$

$3$

$0$