ABSTRACT
Ck2n+1 cos[(2n − 2k + 1)x],
sin2n x = 1
(−1)n−kCk2n cos[2(n − k)x] + 1
sin2n+1 x = 1
(−1)n−kCk2n+1 sin[(2n− 2k + 1)x].
Here n = 1, 2, . . . and Ckm = m!
k! (m− k)! are binomial coefficients (0! = 1).
sin(x± y) = sinx cos y ± cos x sin y,
tan(x± y) = tanx± tan y 1∓ tanx tan y ,
cos(x± y) = cos x cos y ∓ sinx sin y,
cot(x± y) = 1∓ tanx tan y tanx± tan y .
