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Question
Find the value of: tan 15°
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Solution
tan 15° = tan (45° – 30°)
`(tan45° - tan30°)/(1+ tan45°tan30°)` (tan (A-B) = `(tanA-tanB)/(1+tan AtanB)`
`(1 - 1/sqrt(3))/(1 + 1 xx 1/sqrt(3))` .....`(tan pi = 1, tan 30 = 1/sqrt(3))`
= `((sqrt(3) - 1)/sqrt(3))/((sqrt(3) + 1)/sqrt(3))`
= `(sqrt(3) - 1)/(sqrt(3) + 1) xx (sqrt(3) - 1)/(sqrt(3) - 1)`
= `(sqrt(3) - 1)^2/(3 - 1)`
= `(3 + 1 - 2sqrt(3))/2`
= `(4 - 2sqrt(3))/2`
= `2 - sqrt(3)`.
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