If `sin x-cos x =-sqrt2` , then the principal value of `(x-pi/4 )` is

If sinx-cosx=-sqrt(2) the principal value of (x-(pi)/(4)) is

Let f(x)=(cos x -sinx)/(cos 2x)+ sin^2x , x ne pi/4 . The value of f(pi//4) so that f is continuous on (0,pi//2) is (sqrt2=1.41)

If the fundamental period of function f(x)=sin x+cos(sqrt(4-a^(2)))x is 4 pi, then the value of a is/are

Consider the function f(x) = sin^(-1)x , having principal value branch [(pi)/(2), (3pi)/(2)] and g(x) = cos^(-1)x , having principal value brach [0, pi] For sin^(-1) x lt (3pi)/(4) , solution set of x is

Consider the function f(x) = sin^(-1)x , having principal value branch [(pi)/(2), (3pi)/(2)] and g(x) = cos^(-1)x , having principal value brach [0, pi] For sin^(-1) x lt (3pi)/(4) , solution set of x is

Consider the function f(x) = sin^(-1)x , having principal value branch [(pi)/(2), (3pi)/(2)] and g(x) = cos^(-1)x , having principal value brach [0, pi] For sin^(-1) x lt (3pi)/(4) , solution set of x is

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.

log_(sqrt(3))(sin x+2sqrt(2)cos x)>=2,-2 pi<=x<=2 pi then the number of value of x, is