Question

show that 1-cos30/sin30=1-cot60/1+cot60​

Answer 1

Answer:

How can you prove that (1+cot(60o)1−cot(60o))2=1+cos(30o)1−cos(30o) ?

LHS = (1 + Cot 60°/1 - Cot 60°) ^2 = [(1 + 1/root(3))/(1 - 1/root(3))]^2,

= [(root(3) + 1)/(root(3) - 1)]^2,

Rationalize this fraction,

= [(root(3) + 1).(root(3) + 1)/(root(3) - 1).(root(3) + 1)]^2,

= [3 +1 + 2root(3)]/(3 - 1)]^2 = [2 + root(3)]^2,

RHS = (1 + Cos 30° )/ (1 - Cos 30°) = [2 + root(3)]/[(2 - root(3)],

Rationalize this fraction,

= [(2 + root(3)).(2 + root(3))]/[(2 - root(3)).(2 + root(3))],

= [2 + root(3)]^2/(4 - 3) = [2 + root(3)]^2,

LHS =RHS