tan(75°) = (tan60° + tan15°)/(1 - tan60° tan15°)
tan15° = (1-cos30°)/sin30°
now crank it out. You should get 2+√3
Use the sum, difference, double or half-angle formulas to find the exact value of 𝑡𝑎𝑛(75°).
3 answers
Since tan 15° requires extra calculations, try
tan(75) = tan(45 + 30)
= (1 + 1/√3) / (1 - (1)(1/√3)
= (1 + 1/√3) / (1 - 1/√3) * √3 / √3
= (√3 + 1)/(√3 - 1) * (√3 + 1)/(√3 + 1)
= (3 + 2√3 + 1)/2
= 2 + √3
tan(75) = tan(45 + 30)
= (1 + 1/√3) / (1 - (1)(1/√3)
= (1 + 1/√3) / (1 - 1/√3) * √3 / √3
= (√3 + 1)/(√3 - 1) * (√3 + 1)/(√3 + 1)
= (3 + 2√3 + 1)/2
= 2 + √3
well, duh - why did I not see that?
3 answers