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Question
Find the value of tan 15°.
Solution
tan 15° = tan (45° - 30°)
`= (tan 45^circ - tan 30^circ)/(1 + tan 45^circ tan 30^circ)`
`[because tan ("A - B") = (tan "A" - tan "B")/(1 + tan "A" tan "B")]`
`= (1 - 1/sqrt3)/(1 + 1 (1)/sqrt3)`
`= ((sqrt3- 1)/sqrt3)/((sqrt3 + 1)/sqrt3)`
`= (sqrt3 - 1)/cancel(sqrt3) xx cancel(sqrt3)/(sqrt3 + 1)`
`= (sqrt3 - 1)/(sqrt3 + 1) xx (sqrt3 - 1)/(sqrt3 - 1)`
`= (3 + 1 - 2sqrt3)/(3 - 1)`
`= (4 - 2sqrt3)/2`
`= 2 - sqrt3`
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