`f(x)=(sin^(2)x+cos^(4)x)/(cos^(2)x+sin^(4)x)`

If f(x)=(sin^(4)x+cos^(2)x)/(sin^(2)x+cos^(4)x)"for "x in R , then f(2010)

If y=(sin^(4)x-cos^(4)x+sin^(2) x cos^(2)x)/(sin^(4) x+ cos^(4)x + sin^(2) x cos^(2)x), x in (0, pi/2) , then

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 .

Find the number of solutions of sin^(2) x cos^(2)x=1+cos^(2)x+sin^(4) x in the interval [0,pi]

The value of int_(0)^(pi//2) (sin^(3)x cos x)/(sin^(4)x+ cos^(4)x )dx is

(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):}| .

lim_(xtooo) (sin^(4)x-sin^(2)x+1)/(cos^(4)x-cos^(2)x+1) is equal to

f'(sin^(2)x)lt f'(cos^(2)x) for x in

f(x) = sin^(4)x+cos^(4)x in [0,(pi)/(2)]

lim_(xto(pi)) (1-sin(x/2))/(cos(x/2)(cos(x/4)-sin(x/4)))