Consider the following for the next two (02) items that follow :

Given that

sinx + cosx + tanx + cotx + secx + cosecx = 7 

If sin2x = a - b√c, where a and b are natural numbers and c is prime number, then what is the value of a - b + 2c ? 

Consider the following for the next two (02) items that follow :

A quadratic equation is given by

(3 + 2√2)x² - (4 + 2√3)x + (8 + 4√3) = 0

What is the HM of the roots of the equation ? 

Consider the following for the next two (02) items that follow :

A quadratic equation is given by

(3 + 2√2)x² - (4 + 2√3)x + (8 + 4√3) = 0

What is the GM of the roots of the equation ?

Consider the following for the next two (02) items that follow : 

Let Δ(a, b, c, α) = $\left|\begin{array}{ccc} a & b & a \alpha+b \\ b & c & b \alpha+c \\ a \alpha+b & b \alpha+c & 0 \end{array}\right|$

If Δ(a, b, c, α) = 0 for every α > 0, then which one of the following is correct ?