Simplify \(\frac{\sqrt{3}}{\sqrt{3} - 1} + \frac{\sqrt{3}}{\sqrt{3} +1}\)
Simplify \(\frac{\tan 80° - \tan 20°}{1 + \tan 80° \tan 20°}\)
The binary operation * is defined on the set of R, of real numbers by \(x * y = 3x + 3y - xy, \forall x, y \in R\). Determine, in terms of x, the identity element of the operation.
Find the fourth term of the binomial expansion of \((x - k)^{5}\) in descending powers of x.
The tangent to the curve \(y = 4x^{3} + kx^{2} - 6x + 4\) at the point P(1, m) is parallel to the x- axis, where k and m are constants. Find the value of k.
