3h)sin cot'cos tan x=(sqrt(1+x^(2)))/(sqrt(2+x^(2)))

sin cot^(-1)cos (tan ^(-1)x)=sqrt((x^(2)+1)/(x^(2)+2))(x gt 0)

Prove that cos[tan^(-1). {sin (cot^(-1)x)}]=sqrt((1+x^(2))/(2+x^(2))) .

Prove the following: cos{tan^(-1){sin(cot^(-1)x)}}=sqrt((1+x^(2))/(2+x^(2)))

Prove that cos tan^(-1)sin cot^(-1)x=sqrt((x^(2)+1)/(x^(2)+2))

if: f(x)=(sin x)/(sqrt(1+tan^(2)x))-(cos x)/(sqrt(1+cot^(2)x)), then find the range of f(x)

Prove that: sin[cot^(-1){cos(tan^(-1)x)}]=sqrt((x^(2)+1)/(x^(2)+2))cos[tan^(^^)(-1){sin(cot^(-1)x)}]=sqrt((x^(2)+1)/(x^(2)+2))

Assertion: sin(cot^(-1)(1/2))=tan(cos^(-1)x) then the value of x=(sqrt(5))/3 Reason R: cos(tan^(-1)(sin(cot^(-1)x)))=sqrt(((1+x^(2))/(2+x^(2))))

If cos^(-1)x+2sin^(-1)x+3cot^(-1)y+4tan^(-1)y=4sec^(-1)z+5cos ec^(-1)z, then prove that sqrt(z^(2)-1)=(sqrt(1+x^(2))-xy)/(x+y sqrt(1-x^(2)))

Prove that cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2) + 2))