cos^(-1){(cos x+sin x)/(sqrt(2))},-(pi)/(4)

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

Find the derivative of cos^(-1)((sin x +cos x)/(sqrt(2))),(-pi)/(4)lt x lt (pi)/(4) .

Differentiate the following function with respect to x:sin^(-1){(sin x+cos x)/(sqrt(2))}-(3 pi)/(4)

Differentiate cos^(-1) ((sin x + cos x)/(sqrt2)), - (pi)/(4) lt x lt (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.

Prove that cos^-1 ((sin x + cos x )/(sqrt2)) = x - (pi/4), (pi/4) le x le ((5pi)/4)

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

arctan^(-1)((cos x)/(1-sin x))-cos^(-1)(sqrt((1+cos x)/(1-cos x)))=(pi)/(4),x in(0,(pi)/(2))

Simplify: ^(*)sin^(^^)(-1)((sin x+cos x)/(sqrt(2))),backslash-pi/4