If the maximum and minimum values of the determinant
`|(1+sin^(2)x,cos^(2)x,sin2x),(sin^(2)x,1+cos^(2)x,sin2x),(sin^(2)x,cos^(2)x,1+sin2x)|` are `alpha` and `beta` respectively, then `alpha+2beta` is equal to

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

int(sin^(8)x-cos^(8)x)/(1-2sin^(2)x cos^(2)x)dx

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

(i) Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin^(2)x,1+cos^(2)x,4sin2x),(sin^(2)x,cos^(2)x,1+4sin2x):}| . (ii) Let A,B and C be the angles of triangle such that Agt=Bgt=C. Find the minimum value of Delta where Delta=|{:(sin^(2)A,sinAcosA,cos^(2)A),(sin^(2) B,sinBcosB,cos^(2)B),(sin^(2)C,sinCcosC,cos^(2)C):}| .

Find a quadratic polynomial varphi(x) whose zeros are the maximum and minimum values of the function f(x)=|(1+sin^2x, cos^2x,sin2x) ,(sin^2x,1+cos^2x,sin2x), (sin^2x ,cos^2x,1+sin2x)|

int(sin2x)/((1+cos2x)^(2))dx

int(1+sin2x)/(cos^2x)dx

Find a quadratic polynomial phi(x) whose zeros are the maximum and minimum values of the function: f(x)=|[1+sin^2x,cos^2x,sin2x],[sin^2x,1+cos^2x,sin2x],[sin^2x,cos^2x,1+sin2x]|

Solve (1+sin^2x-cos^2x)/(1+sin^2x+cos^2x)

Solve (sin^(2) 2x+4 sin^(4) x-4 sin^(2) x cos^(2) x)/(4-sin^(2) 2x-4 sin^(2) x)=1/9 .