[" EXAMPLE 7Simplify each of the following: "],[" (i) "sin^(-1)((sin x+cos x)/(sqrt(2)))+(pi)/(4)

Simplify each of the following: sin^(-1)((sin x+cos x)/(sqrt(2)))

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

Simplify each of the following: sin^(-1)((sinx+cosx)/(sqrt(2))),\ pi/4

Simplify each of the following: sin^(-1)((sinx+cosx)/(sqrt(2))),\ pi/4 < x < (5pi)/4 (ii) cos^(-1)((sinx+cosx)/(sqrt(2))), (5pi)/4 < x < (9pi)/4

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

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

Find the principal value of each of the following: sin^(-1)((sqrt(3)+1)/(2sqrt(2))) (ii) sin^(-1)(cos(pi/4)) (iii) sin^(-1)(tan((5pi)/4))

Find the principal value of each of the following: sin^(-1)((sqrt(3)+1)/(2sqrt(2)))( (ii) sin^(-1)((cos(3 pi))/(4))( iii) sin^(-1)((tan(5 pi))/(4))

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

cos x-sin x = sqrt (2) cos (x + (pi) / (4))