Gf(x)=4cos sqrt(x)-(pi)/(9)

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

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

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

int((e^(sqrt(x))-e^(-sqrt(x)))cos(e^(sqrt(x))+e^(-sqrt(x))+(pi)/(4))+(e^(sqrt(x))+e^(-sqrt(x)))cos(e^(sqrt(x))-e^(-sqrt(x))+(pi)/(4)))/(sqrt(x))

If pi

Find the number of solution(s) of the equation cos (pi sqrt(x)) cos (pi sqrt(x-4))=1 .

Find the number of solution(s) of the equation cos (pi sqrt(x)) cos (pi sqrt(x-4))=1 .

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)

Differentiate the functions with respect to x:cos^(-1){(cos x+sin x)/(sqrt(2))},-(pi)/(4)