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 :

Let P(x) = ((1- cos 2 x + sin 2x)/(1+ cos2x + sin2x))^(2) + ((1+ cot x + cot^(2) x)/( 1+ tan x+ tan^(2) x) ) , then the minimum value of P(x) equals

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

Solve 2sinx+cos2x+2sin^(2)x-1 for 0 le x le 2pi .

int_(0)^((pi)/(4))(dx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)=(1)/(ab)tan^(-1).(b)/(a)(a,bge0)

Solve: 2 (cos x + cos 2x) + sin 2x (1 + 2 cos (x))=2 sinx,-pi le x le pi .

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 ?

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