Question

Prove that:-cot^-1(theta)=cos^-1(theta)/ √1+(theta)² ?

Answer 1

Let `cot^(-1)theta=A` then

`rarrcotA=theta`

`rarrtanA=1/theta`

`rarrcosA=1/secA=1/sqrt(1+tan^2A)=1/sqrt(1+(1/theta)^2)`

`rarrcosA=1/sqrt((1+theta^2)/theta^2)=theta/sqrt(1+theta^2)`

`rarrA=cos^(-1)(theta/(sqrt(1+theta^2)))=cot^(-1)(theta)`

`rarrthereforecot^(-1)(theta)=cos^(-1)(theta/(sqrt(1+theta^2)))`