Question

prove that (cos 15 degree+sin 15 degree)/(cos 15 degree-sin15degree)=root3

Answer 1

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

=(cos (90-75)+cos15)/(cos (90-75)-sin15)

=(sin75+sin15)/(sin75-sin15)

=2sin45.cos30/2cos45.sin30

=cos30/sin30=cot30=root3= RHS

Answer 2

rationalize
=
(cos15+sin15)(cos15+sin15)÷[(cos15-=sin15)(cos15+sin15)],,,
=[cos²15+sin²15+2sin15cos15]÷[cos²15-sin²15]
=[1+sin30]÷[cos30]
=[1+1/2]÷(√3/2)
=3/2÷√3/2
=3/√3
=(√3√3)/√3=√3