If `|[sin2x,cos^2x,cos4x],[cos^2x,cos2x,sin^2x],[cos^4x,sin^2x,sin2x]|=a_0+a_1 (sinx)+a_2(sin^2x)+....+a_n(sin^n x)` then the value of `a_0` is-

if sin x + sin^2 x = 1 , then the value of cos^2 x + cos^4x is

if sin x + sin^2 x = 1 , then the value of cos^2 x + cos^4x is

If the determinant |(cos2x,sin^2 x,cos 4x),(sin^2 x,cos 2x,cos^2 x),(cos 4x,cos^2 x,cos 2x)| is expanded in powers of sin x , then the constant term is

If sinx+sin^2x+sin^3x=1 then find the value of cos^6x-4cos^4x+8cos^2x

If sinx+sin^2x+sin^3x=1 then find the value of cos^6x-4cos^4x+8cos^2x

(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):}| .

Prove that (cos4x+cos3x+cos2x)/(sin4x+sin3x+sin2x)=cot3x

Compute the following: [[cos^2x, sin^2x],[sin^2 x, cos^2 x]]+[[sin^2x, cos^2 x],[cos^2 x, sin^2 x]]

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

If cos4x=a_0+a_1cos^2x+a^2cos^4x is true for all values of x in R , then the value of 5a_0+a_1+a_2 is_______