" 5."sin(cot^(-1)x)=?

cos[tan^(-1) {sin(cot^(-1) x)}] =

If sin (cot^(-1)(1-x))=cos(tan^(-1)(-x)) , then x is

If sin(cot^(-1)(x+1))=costan^(-1)x , then x=

Evaluate: sin(cot^(-1)x)

Evaluate: i) sin{pi/3-sin^(-1)(-1/2)} ii) sin(1/2cos^(-1)4/5) iii) sin(cot^(-1)x) iv) tan1/2(cos^(-1)sqrt(5)/3)

Statement 1: If x=(1)/(5 sqrt(2)) , then [x cos(cot^(-1)x)+sin(cot^(-1)x)]^(2)=(51)/(50) . Statement 2: tan["cot"^(-1)(1)/(5sqrt(2))-"sin"^(-1)(4)/(sqrt(17))]=(29)/(3) .

Statement 1: If x=(1)/(5 sqrt(2)) , then [x cos(cot^(-1)x)+sin(cot^(-1)x)]^(2)=(51)/(50) . Statement 2: tan["cot"^(-1)(1)/(5sqrt(2))-"sin"^(-1)(4)/(sqrt(17))]=(29)/(3) .

The value of sin (cot^(-1)x) is :

cos [ tan^(-1){sin (cot^(-1)x)}] =