Question

Show that (√3+1)(3-cot30) is equal to tan cube 60 minus 2 sin 60

Answer 1

To prove: (√3+1)(3−cot30°)=tan^360°−2sin60°

LHS=(√3+1)(3−cot30°)
=(√3+1)(3−√3)
=3√3−3+3−√3
=2√3
RHS=tan^360°−2sin60°
=(√3)^3−2(√3/2)=3√3−√3=2√3
∴LHS=RHS.
Hence proved