IIT JEE , AIEEE Forum - Mathematics , Trignometry

man111

(1) Sin⁸ (10⁰) +sin⁸ (130⁰) +sin⁸(250⁰) =93/128.

how can i solve these type question???????????????????

konichiwa2x

Let

. These three angles all have the property that

. Since

, it follows that a, b and c are the solutions of the equation

, or

.

Therefore

and

. From that, you can obtain the formulas for sums of powers of roots:

,

,
and finally

.

konichiwa2x

you can use complex numbers also to solve this...but it gets a bit tedious.

konichiwa2x

here is the method for those who asked..but the previous one is much better...

from

and DeMoivre

Substitute x=10, x=250, and x=130 , simplify etc and

for

u'll ge,

since