tan (cos^-1(1/3)) = ???

Question

 I have to find the exact value for this expression.

Answer 1

Draw a right triangle with lower acute angle being θ = cos^-1(1/3)

 

|\

|  \

|    \

|      \

|        \

| √8     \ 3

|            \

|              \

|                \

|               θ \

         1

 

 

From here we see the answer.

 

tan cos^-1 (1/3) = tan θ = √8 = 2√2