Question

prove that cos75°+cos15°/sin75°-sin15°=√3​

Answer 1

Answer:

sin75=sin(30+45)=sin30cos45+sin45cos30

=1/2×1/√2+1/√2×√3/2

=1/2√2+√3/2√2

=(1+√3)/2√2

sin15=sin(45-30)=sin45cos30-sin30cos45

sin15=(√3-1)/2√2

similarly

cos75=(√3-1)/2√2

cos15=(√3+1)/2√2

sin75-sin15/cos75+cos15

=(1/2√2+√3/2√2-√3/2√2+1/2√2)÷(√3/2√2-1/2√2+√3/2√2+1/2√2)

=(-2/2√2)÷(2√3/2√2)

=(-1/√2)÷(√3/√2)

=-1/√3