Răspuns:
tg15⁰=sin15⁰/cos15⁰
=sin(60⁰-45⁰)/cos(60⁰-45⁰)
=(sin60⁰cos45⁰-cos60⁰sin45⁰) / (cos60⁰cos45⁰+sin60⁰sin45⁰)
=(√3/2×√2/2-1/2×√2/2) / (1/2×√2/2+√3/2×√2/2)
=(√6/4-√2/4)/(√2/4+√6/4)
=(√6-√2)/4 / (√6+√2)/4
=(√6-√2) / (√6+√2)
raționalizăm
=(√6-√2)²/(6²-2²)
=(6-2√12+2)/(36-4)
=(10-2×2√3)/32
=(10-4√3)/32
=2(5-2√3)/32
=(5-2√3)/16
=5/16-√3/8
