$${\tan ^{ - 1}}\left( {{{1 + \sqrt 3 } \over {3 + \sqrt 3 }}} \right) + {\sec ^{ - 1}}\left( {\sqrt {{{8 + 4\sqrt 3 } \over {6 + 3\sqrt 3 }}} } \right)$$ is equal to :

Let $$y = y(x)$$ be the solution of the differential equation $${x^3}dy + (xy - 1)dx = 0,x > 0,y\left( {{1 \over 2}} \right) = 3 - \mathrm{e}$$. Then y (1) is equal to

Let $$\Omega$$ be the sample space and $$\mathrm{A \subseteq \Omega}$$ be an event.

Given below are two statements :

(S1) : If P(A) = 0, then A = $$\phi$$

(S2) : If P(A) = 1, then A = $$\Omega$$

Then :

The area enclosed by the curves $${y^2} + 4x = 4$$ and $$y - 2x = 2$$ is :