[" 34.FHes andritit for "],[qquad tan^(-1)a+tan^(-1)b=cos^(-1)[(1-ab)/(sqrt((1+a^(2))(1+b^(2))))]]

Prove that : tan^(-1) a - tan^(-1) b = cos ^(-1) [(1+ab)/(sqrt((1+a^(2))(1+b^(2))))]

Prove that : tan^(-1) a - tan^(-1) b = cos ^(-1) [(1+ab)/(sqrt((1+a^(2))(1+b^(2))))]

Prove that, tan^(-1)a+tan^(-1)b+tan^(-1)((1-a-b-ab)/(1+a+b-ab))=(pi)/(4) .

Prove that 2tan^(-1)sqrt((b)/(a))=cos^(-1)((a-b)/(a+b))

The expression (1)/(sqrt(2)){(sin tan^(-1)cos tan^(-1)t)/(cos tan^(-1)sin cot^(-1)sqrt(2)t)}*{sqrt((1+2t^(2))/(2+t^(2)))}

tan[tan^(-1)(1/(a+b))+tan^(-1)(b/(a^(2)+ab+1))]=

sin^(-1) ""(2a)/(1+a^(2))-cos^(-1) ""(1-b^(2))/(1+b^(2))=2tan ^(-1) ""(a-b)/(1+ab)

Which of the following is/are correct? tan[cos^(-1)(4)/(5)+tan^(-1)(2)/(3)]=(17)/(6)cos[tan^(-1)(1)/(3)+tan^(-1)(1)/(2)]=(1)/(sqrt(2))cos2tan^(-1)((1)/(3))+cos(tan^(-1)2sqrt(2))=(14)/(15)cos[2cos^(-1)(1)/(5)+sin^(-1)(1)/(5)]=-(2sqrt(6))/(6)

tan(A/2)=(sqrt((1-cos A)/(1+cos A)))

The value of tan^(-1)((sqrt(3))/(2))+tan^(-1)((1)/(sqrt(3))) is equal to a) tan^(-1)((5)/(sqrt(3))) b) tan^(-1)((2)/(sqrt(3))) c) tan^(-1)((1)/(2)) d) tan^(-1)((1)/(3sqrt(3)))