Find the binomial expansion of √1x in increasing power of x up to the term in x⁴

(b)(i) prove that the trigonometric identity_____1_____ _____cot²x______=cos²(1 tan²x) ² (1 cot²x) ²
(b)(ii) Find all values of Z=64³?

2 answers

If you mean √(1+x) then that's
(1+x)^(1/2) = 1^(1/2)*x^0 + (1/2)*1^(-1/2)*x^1 + ... + (1/2)(-1/2)(-3/2)(-5/2)*1^(-7/2)*x^4 + ...
= 1 + x/2 - x^2/8 + x^3/16 - 5x^4/128 + ...

(bi) How about some + and - signs in there? If there's a fraction involved, use / and () to disambiguate.

(bii) I assume you mean 64^(1/3).
That would be 4cis(2kπ/3) for all integer k
How about a complete expression of the problem solution