Use the principle of mathematical induction to prove the following:
cosθ + cos3θ + cos5θ ... + cos(2n-1)θ = [sin 2nθ]/[2sinθ] for all positive n
sinθ + sin3θ + sin5θ ... + sin(2n-1)θ = [1-cos2nθ]/[2sinθ] for all positive n
1 + cisθ + cis2θ ... + cis nθ = [1-cis(n+1)θ] / [1-cisθ] where cisθ doesn't equal 1, n is greater than or equal to 1
I have solved these for n=1, so i said P(k)=1 is true (n=k), but now I am onto P(k)= k+1, and I am really stuck!
Any help would be greatly appreciated!
Thanks in advance =]