Question

sa se arate ca sin 105* =√6+√2 totul supra 2

Answer 1

[tex]\it sin 105^o = sin(60^o+ 45^o) = sin60^o cos45^o+sin45^ocos60^o= \\\;\\ \\\;\\ = \dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2} + \dfrac{\sqrt2}{2}\cdot\dfrac{1}{2} = \dfrac{\sqrt6}{4} + \dfrac{\sqrt2}{4} = \dfrac{\sqrt6+\sqrt2}{4} [/tex]