`sin x+ cos x=1/sqrt(2)`, then find `x`.

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

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

If f(x)=cos^(-1)((1)/(sqrt(13)))(2cos x-3sin x)+sin^(-1)((1)/(sqrt(13)))(2cos x+3sin x)wdot rt sqrt(1+x^(2)) then find (df(x))/(dx) at x=(3)/(4)

if: f(x)=(sin x)/(sqrt(1+tan^(2)x))-(cos x)/(sqrt(1+cot^(2)x)), then find the range of f(x)

Evaluate the following integrals. int (sin x + cos x)/(sqrt(1+ sin 2x))dx

Evaluate int((x cos x+1)dx)/(sqrt(2x^(3)e^(sin x)+x^(2)))

If "sin" x + "sin"^(2) x = 1 show that: cos^(4)x + cos^(2)x = 1 (ii) If "sin" x + cos x =sqrt(2) cos x show that: sqrt2 sin x = cos x - sin x

int(2sin x)/((3+sin2x))dx is equal to (1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(2sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(4)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+cnone of these

y=sqrt(sin +cos x+sqrt(sinx+ cos x +sqrt(sin x +cos x +....oo))) " then find " dy/dx