" 2."cot^(-1)[(1+cos x)/(sin x)]=(x)/(2)

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

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

If [ x cos ( cot^(-1) x ) + sin ( cot^(-1) x) ]^(2) = (51)/(50) then the positive value of x is

Integrate the following with respect to x. (i) 1/(cos^2x) " " (ii) (cot x)/(sin x) " " (iii) (sin x)/(cos^2 x) " " (iv) 1/(sqrt(1 - x^2)) .

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))

Prove that (i).(sin 2x)/(1-cos 2x) = cot x" " (ii) .(1- cos 2x)/(1+ cos 2x) = tan^(2) x

Prove that: (1+cos4x)/(cot x-tan x)=(1)/(2)sin4x

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

(cos2x-1)cot^(2)x=-3sin x