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Question
Find the value of the following:
cot 75°
Solution
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)`
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