cos `2x + 2sin^(2)` x =1

If maximum and minimum values of the determinant |{:(1 + cos^(2)x , sin^(2) x, cos 2x),(cos^(2) x , 1 + sin^(2)x, cos 2x),(cos^(2) x , sin^(2) x , 1 + cos 2 x):}| are alpha and beta then

Let m and M be respectively the minimum and maximum values of |{:(cos^(2) x , 1+sin^(2) x , sin 2x),(1+cos^(2)x, sin^(2)x, sin 2x),(cos^(2) x , sin^(2)x, 1+ sin2x):}| Then the ordered pari ( m , M) is equal to :

The equation 8cos^(4) x/2 sin^(2) x/2 =x^(2) +1/x^(2), x int (0,4pi] holds for

sin ^ (2) x, cos x ^ (2) x, 1cos ^ (2) x, sin ^ (2) x, 1-10,12,2] | = 0

If alpha and beta respectively the minmum and minimum values of the fuction f(x) given by f(x)=|{:(1+sin^2" " x cos^2x " " sin2x),(sin^2x " "1+cos^2 x " "sin 2x),(sin^2x " "cos^2x" "1+sin 2x):}| then which one of the following options is not true ?

sum of all the solutions of the equation cos2x+sin^(2)2x=1 which lie in the interval [0,2 pi] is equal to

The equation 8 cos^(4) x/2 sin^(2)x/2= x^(2) +1/x^(2), x int (0,4pi] holds for

(1-cos 2x + sin x)/(sin 2x + cos x) = tan x