Question

Find the value of the following:

cot 75°

Answer 1

cot 75° = `1/(tan 75^circ)`

Consider tan 75° = tan (30° + 45°)

`= (tan 30^circ + tan 45^circ)/(1 - tan 30^circ tan 45^circ)`

`= (1/sqrt3 + 1)/(1 - (1/sqrt3) xx 1)`

`= ((1 + sqrt3)/sqrt3)/(1 - 1/sqrt3)`

`= (((1 + sqrt3)/sqrt3))/(((sqrt3 - 1)/sqrt3))`

`= (1 + sqrt3)/sqrt3 xx sqrt3/(sqrt3 - 1)`

`= (sqrt3 + 1)/(sqrt3 - 1)`

cot 75° = `1/(tan 75^circ) = (sqrt3 + 1)/(sqrt3 - 1)`