The value of expression (sin theta+3sin3...

The value of expression `(sin theta+3sin3 theta+5sin5 theta+3sin7 theta)/(sin2 theta+2sin4 theta+3sin6 theta)` where `theta=(4 pi)/(5)` is equal to

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sin theta + sin3 theta + sin5 theta = 0

Solve 4sin theta sin2 theta sin4 theta=sin3 theta

(sin7 theta+6sin5 theta+17sin3 theta+12sin theta)/(sin6 theta+5sin4 theta+12sin2 theta)

(sin7 theta+6sin5 theta+17sin3 theta+12sin theta)/(sin6 theta+5sin4 theta+12sin2 theta)=

sin3 theta=4sin theta sin2 theta sin4 theta in0<=theta<=pi has

The value of the expression (sin3 theta+sin5 theta+sin7 theta+sin9 theta)/(cos3 theta+cos5 theta+cos7 theta+cos9 theta) when theta=(pi)/(18) is

(sin theta+2sin3 theta+sin5 theta)/(sin3 theta+2sin5 theta+sin7 theta)=(sin3 theta)/(sin5 theta)

(sin5 theta-2sin3 theta + sin theta) / (cos5 theta-cos theta) = tan theta