Answer:
2 + √3.
Step-by-step explanation:
tan 75 = tan (45 + 30)
= (tan 45 + tan 30) / (1 - tan 45 tan 30)
= ( 1 + 1/√3) / (1 - 1*1/√3)
= (1 + √3) / √3 * √3 / (√3 - 1)
= √3 + 1/ √3 - 1
Multiply top and bottom by √3 + 1;
= (√3 + 1)(√3 + 1) / (√3 - 1)(√3 + 1)
= 3 + 2√3 + 1 / (3 - 1)
= (4 + 2√3) / 2
= 2 + √3.
