Question

Solve the following equation for x:  `cos (tan^(-1) x) = sin (cot^(-1)  3/4)`

Answer 1

The given equation is `cos (tan^(-1) x) = sin (cot^(-1)  3/4)`

`cos (tan^(-1) x) = sin(cot^(-1)  3/4)`

`=> cos (tan^(-1) x) = cos(pi/2 - cot^(-1)  3 /4)`              `[sintheta = cos(pi/2 - theta)]`

`=> cos(tan^(-1) x) = cos(tan^(-1)  (3/4))`         `(tan^(-1) x + cot^(-1) x = pi/2)`

`=> tan^(-1) x = tan^(-1) (3/4)`

`=> x = 3/4`