Question

find the value of cot15​

Answer 1

Answer:

cot(A - B) = cotA cotB + 1/ cotB - cotA

cot15 = cot(60 - 45)

= cot60 cot45 + 1/ cot45 - cot 60

= 1/√3 + 1 / 1 - 1/√3

= 1+ √3 / √3 - 1

= √3 + 1 / √3 - 1

= (√3 + 1)(√3 + 1) / (√3 - 1)(√3 + 1)

= 3 + 1 + 2√3 / 3 - 1

= 4 + 2√3 / 2

= 2 + √3