Question-7125

Question Number 7125 by Tawakalitu. last updated on 11/Aug/16

Commented by Tawakalitu. last updated on 11/Aug/16

I h a v e s e e n a s o l u t i o n t o t h i s q u e s t i o n

Answered by sandy_suhendra last updated on 13/Aug/16

[c o s \frac{π}{7} + c o s \frac{3 π}{7} + c o s \frac{5 π}{7}] \times \frac{2 s i n \frac{π}{7}}{2 s i n \frac{π}{7}}

= \frac{2 s i n \frac{π}{7} c o s \frac{π}{7} + 2 s i n \frac{π}{7} c o s \frac{3 π}{7} + 2 s i n \frac{π}{7} c o s \frac{5 π}{7}}{2 s i n \frac{π}{7}}

2 s i n A c o s B = s i n (A + B) + s i n (A - B)

s i n (- A) = - s i n A

= \frac{s i n \frac{2 π}{7} + s i n 0 + s i n \frac{4 π}{7} - s i n \frac{2 π}{7} + s i n \frac{6 π}{7} - s i n \frac{4 π}{7}}{2 s i n \frac{π}{7}}

= \frac{s i n \frac{6 π}{7}}{2 s i n \frac{π}{7}} = \frac{s i n [π - \frac{π}{7}]}{2 s i n \frac{π}{7}} = \frac{s i n \frac{π}{7}}{2 s i n \frac{π}{7}} = \frac{1}{2}

Commented by Rasheed Soomro last updated on 15/Aug/16

G^{OO} D A p p r o a c h!