1-sin60:cos60=1-Tan30:1+Tan30

Step-by-step explanation:

LHS = (1-sin60) / cos60

= (1-√3:2) / 1:2

=2 (1-√3:2)

=2-√3

RHS = (1-tan30) / (1+tan30)

={1 - (1:√3) }/{1 + (1:√3) }

={ (√3-1) / √3}/{ (√3+1) / √3}

= (√3-1) / (√3+1)

={ (√3-1) (√3-1) }/{ (√3+1) (√3-1) }

= (3-√3-√3+1) / (3-1)

= (4-2√3) / 2

=2-√3

Therefore LHS=RHS