The value of sin (π/18)+sin (π/9)+sin (2π /9)+sin (5π/18) is given by

Question

The value of sin (π/18)+sin (π/9)+sin (2π /9)+sin (5π/18) is given by (A) sin (7π/18)+sin (4π/9) (B) 1 (C) cos (π/6)+cos (3π/7) (D) cos (π/9)+sin (π/9)

Tardigrade Admin · Accepted Answer

We have, sin (π/18)+sin (π/9)+sin (2π /9)+sin (5π/18) =sin(π-(17π/18))+sin(π -(8π /9))+sin (2π/9)+sin (5π/18) =sin (17π/18)+sin (8π /9)+sin (2π /9)+sin (5π/18) =(sin (17π /18)+sin (5π /18))+(sin (8π /9)+sin (2π /9)) =2 sin((11π/18))cos (π/3)+2 sin (5π/9) cos (π/3) =sin (11π /18)+sin (5π /9) =sin(π-(7π/18))+sin(π-(4π/9)) =sin (7π /18)+sin (4π /9)

Q. The value of $s in \frac{π}{18} + s in \frac{π}{9} + s in \frac{2 π}{9} + s in \frac{5 π}{18}$ is given by

$s in \frac{7 π}{18} + s in \frac{4 π}{9}$

$1$

$cos \frac{π}{6} + cos \frac{3 π}{7}$

$cos \frac{π}{9} + s in \frac{π}{9}$

Q. The value of sin18π​+sin9π​+sin92π​+sin185π​ is given by

sin187π​+sin94π​

1

cos6π​+cos73π​

cos9π​+sin9π​

Q. The value of $s in \frac{π}{18} + s in \frac{π}{9} + s in \frac{2 π}{9} + s in \frac{5 π}{18}$ is given by

$s in \frac{7 π}{18} + s in \frac{4 π}{9}$

$1$

$cos \frac{π}{6} + cos \frac{3 π}{7}$

$cos \frac{π}{9} + s in \frac{π}{9}$