- #1

songoku

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- Homework Statement
- a. Find sum of (sin theta)^3 + 1/3 (sin 3 theta)^3 + .... + 1/3^n (sin (3^n theta))^3 using 4 (sin theta)^3 = 3 sin theta - sin (3 theta)

b. Using above result, prove:

(sin theta)^2 cos (theta) + (sin 3 theta)^2 cos (3 theta) + ... + (sin (3^n theta))^2 cos (3^n theta) = 1/4 cos theta - 1/4 cos (3^(n+1) theta)

- Relevant Equations
- Not sure

I got answer to (a), which is 3/4 sin thteta - sin ((3^(n+1)) theta) / (4 . 3^n) but I do not know how to use this result to prove next question.

I tried to change theta into pi/2 - theta so that sin change to cos or vice versa but not working.

Thanks

I tried to change theta into pi/2 - theta so that sin change to cos or vice versa but not working.

Thanks