Buktikan Tan 75°=2+akar3

Tan75°
= Tan(30°+45°)
= (tan30° + tan45°) / (1 - tan30° . tan45°)
= (√3/3 + 1) / (1 - √3/3)
= ((3 + √3)/3) / ((3 - √3)/3)
= (3 + √3) / (3 - √3)
= (3 + √3)(3 + √3) / (3 - √3)(3 + √3)
= (9 + 6√3 + 3) / 6
= (12 + 6√3) / 6
= 2 + 2√3