`sin x+cos x=sqrt(2)`

The values of a for which the equation sqrt(a)sin x-2cos x=sqrt(2)+sqrt(2-a) has solutions are

If I=int(sqrt(cot x)-sqrt(tan x))dx, then I equal sqrt(2)log(sqrt(tan x)-sqrt(cot x))+Csqrt(2)log|sin x|cos x+sqrt(sin2x)|+Csqrt(2)log|sin x-cos x+sqrt(2)sin x cos x|+sqrt(2)log|sin(x+(pi)/(4))+sqrt(2)sin x cos x|+C

If sin x+ cos x = sqrt2 sin x , then the value of tan x is:

Number of solutions of the equation sin x + cos x-2sqrt(2) sin x cos x=0 for x in [0, pi] is

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

Range of the function f(x)=log_(2)((sin x+cos x+3sqrt(2))/(sqrt(2))) is given by

Find the range of f(x)=log_(2)((sin x-cos x+3sqrt(2))/(sqrt(2)))

Number of real value of x satisfying the equation |sin x cos x|+sqrt(2+tan^(2)x+cot^(2)x)=sqrt(3)in[0,2 pi]

Number of roots of the equation |sin x cos x|+sqrt(2+tan^(2)x+cot^(2)x)=sqrt(3),x in[0,4 pi] are