sin^(-1)((4cos x+5sin x)/(sqrt(41)))

The differential coefficient of sin^(-1)((4sin2x+3cos2x)/(5)) with respect to cos^(-1)((5cos x-4sin x)/(sqrt(41))) is -2b*-1c.1d

The differential coefficient of sin^(-1)((4sin2x+3cos2x)/5) with respect to cos^(-1)((5cos x-4sin x)/(sqrt(41))) is -2 b. -1 c. 1 d. 2

The differential coefficient of sin^(-1)((4sin2x+3cos2x)/5) with respect to cos^(-1)((5cos x-4sin x)/(sqrt(41))) is -2 b. -1 c. 1 d. 2

The differential coefficient of sin^(-1)((4sin2x+3cos2x)/5) with respect to cos^(-1)((5cos x-4sin x)/(sqrt(41))) is -2 b. -1 c. 1 d. 2

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

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

Differentiate the following w.r.t. x : sin^-1((4sinx+5cosx)/sqrt41)

f(x)=sqrt(sin(cos x))+ln(-2cos^(2)x+3cos x+1)+e^(cos^(-1))((2sin x+1)/(2sqrt(2sin x)))