Simplify each of the following: `cos^(-1)(3/5cosx+4/5sinx)` , where `-(3pi)/4lt=xlt=pi/4`

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

cos^(-1)((3cosx-4sinx)/(5))

Evaluate each of the following cos^(-1) (cos""(5pi)/(4))

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

cos^(-1)((sinx+cosx)/(sqrt(2))),-(pi)/(4) ltx lt(pi)/(4)

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

Simplify tan^(-1).(cosx/(1-sinx))(-pi)/2 lt x lt pi/2

Express each of the following in the simplest form: tan^(-1){(cosx)/(1-sinx)},\ -pi/2

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

Differentiate the following w.r.t. x : (sinx-cosx)^(sinx-cosx),pi/4ltxlt(3pi)/4