Question

prove that:

cot (15/2) = 61/2 + 41/2 + 31/2 + 21/2

Answer 1

Best Answer: cot(15/2)°
= cos(15/2)° / sin(15/2)°
= 2cos^2 (15/2)° / 2sin(15/2)° cos(15/2)°
= (1 + cos15°)/sin15°
Plugging cos15° = (1/4) (√6 + √2) and sin15° = (1/4) (√6 - √2)
= [1 + (1/4) (√6 + √2)] / [(1/4) (√6 - √2)]
= (4 + √6 + √2) / (√6 - √2)
= [(4 + √6 + √2) * (√6 + √2)] / [(√6 - √2) * (√6 + √2)]
= (4√6 + 6 + 2√3 + 4√2 + 2√3 + 2) / 4
= (4√2 + 4√3 + 8 + 4√6) / 4
= √2 + √3 + √4 + √6.
this is my answer!!!