- #1
songoku
- 2,315
- 330
- 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