Question

cot15°+1/cot15°-1=?

Answer 1

(cot15°+1)/(cot15°-1)

=(cos15°/sin15+1)/(cos15°/sin15-1)

=(cos15+sin15)/(cos15-sin15)

=(cos15+sin15)(cos15+sin15)/[(cos15-sin15)(cos15+sin15)]

=(cos^2 15+sin^2 15+2cos15sin15)/(cos^2 15-sin^2 15)

=(1+sin30)/cos30

=(1+1/2)/(√3/2)

=√3