Question

need your help friends plzzzzzzz help........
evaluate cot105°-tan105°​

Answer 1

Answer:

2√3

Step-by-step explanation:

cot105° - tan105° = cot(60+45)° - tan(60+45)°

=>[(cot60°.cot45°-1)/(cot60°+cot45°)] - [(tan60°+tan45°)/(1-tan60°.tan45°)]

=> [(1- √3)/(1+√3)] - [(1+ √3)/(1- √3)]

=> [(1- √3)/(1+√3)] + [(1+ √3)/(√3 - 1)]

=>[(√3 -1–3+√3 + 1+3+2√3)/(3–1)]

=>[4√3/2]

=>2√3