4cos sqrt(x^(2)-(pi)/(9))

Let f(x)=4cos sqrt(x^(2)-(pi^(2))/(9)) Then the range of f(x) is

cos^(-1)((sin x+cos x)/(sqrt(2))),(pi)/(4) lt x lt (5pi)/4

If pi

tan ((11 pi) / (3)) - 2sin ((9 pi) / (3)) - (3) / (4) cos ec ^ (2) ((pi) / (4)) + 4cos ^ ( 2) ((17 pi) / (6)) = (3-2sqrt (3)) / (2)

If x in((3 pi)/(2),2 pi), then 4cos^(2)((pi)/(2)-x)+4sqrt(cos2x+sin^(4)x) equals

lim_(x rarr pi/4)(sqrt(cos x)-sqrt(sin x))/(x-(pi)/(4))

Prove that : int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)

Prove that : int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)

sin ((5 pi) / (18)) - cos ((4 pi) / (9)) = sqrt (3) sin ((pi) / (9))

Over [-pi,pi] the solution of 2sin^(2)(x+(pi)/(4))+sqrt(3)cos2x>=0 is