I have been doing some questions on Binomial Series expansion and have been stuck on this particular question for a long time and desperately need some guidance. Q) Expand (1/(sqrt(1-b^2(sin^2)x)))), where b = sin(1/2(theta)) as a binomial series. Here is what I have done so far... Let x = (b^2(sin^2)x) because I want the expression in binomial form. So it becomes 1/sqrt(1 - x) with k = -1/2 (1-x)^-1/2 can be written in binomial form... (S is capital sigma) = S(-1/2 n)(-x)^n = 1 + (-1/2)(-x) + ((-1/2)(-3/2)/2!)*(-x)^2 + ... = 1 + 1/2x - 3/8x^2 + ... = 1 + 1/2k^2sin^2x - 3/8k^4sin^4x + ... Any help on this question would be excellent!