Find the angle between two vectors and with magnitudes 1 and 2 respectively and when

Prove that the curves y² = 4x and x² = 4y divide the area of the square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.

Evaluate:

Using properties of determinants, prove the following:

Differentiate the following function w.r.t. x:

(x)^{cos x} + (sin x)^{tan x}