If` sin 2x= 2024/2025` where `5pi/4< x <9pi/4`, the value of the sin x - cos x is equal to

Show that tan^-1((cosx)/(1 + sin x)) = pi/4 - x/2 , where x in (-pi/2 , pi/2)

range of sin[x] where -(pi)/(4)<=x<=(pi)/(4)

Simplify each of the following: cos^(-1)((3)/(5)cos x+(4)/(5)sin x), where -(3 pi)/(4)<=x<=(pi)/(4)

Express sin^(-1)((sin x+ cos x)/(sqrt2)) , where -(pi)/(4) lt x lt (pi)/(4) , in the simplest form.

Express sin^(-1)((sin x+ cos x)/(sqrt2)) , where -(pi)/(4) lt x lt (pi)/(4) , in the simplest form.

int(sin^(3)x cos^(5)x-cos^(3)x sin^(5)x)ln(sin2x)*dx=f(x), where f((pi)/(4))=-(1)/(256) then the value of f((5 pi)/(4)) equals

What is (d sqrt(1-sin2x))/(dx) equal to,where (pi)/(4)

If |x^(2)-1+sin x|=|x^(2)-1|+|sin x| where x in [-2 pi,2 pi]

|x^(2)-1+sin x|=|x^(2)-1|+|sin x| where x in [-2 pi,2 pi]

If f(x) is continuous at x= pi/4 , where f(x)=(sin 2x)^(tan^(2)2x) , for x != pi/4 , then f(pi/4)=