Folosim formulele:
[tex]sin (a) + sin (b) = \\ = 2 \times sin( \frac{a + b}{2} ) \times cos( \frac{a - b}{2} ) \\ \\ [/tex]
[tex]sin (a) - sin (b) = \\ = 2 \times sin( \frac{a - b}{2} ) \times cos( \frac{a + b}{2} ) \\ \\ [/tex]
[tex]cos (a) + cos (b) = \\ = 2 \times cos( \frac{a + b}{2} ) \times cos( \frac{a - b}{2} ) \\ \\ [/tex]
[tex]cos (a) - cos (b) = \\ = - 2 \times sin( \frac{a + b}{2} ) \times sin ( \frac{a - b}{2} ) \\ \\ [/tex]
a) sin(15) + sin(75) = sin(75) + sin(15) =
= 2 • sin(75+15/2) • cos(75-15) =
= 2 • sin(90/2) • cos(60/2) =
= 2 • sin(45) • cos(30) =
= 2 • ✓2/2 • ✓3/2 =
= ✓6/2
b) sin(75) - sin(15) =
= 2 • sin(75-15/2) • cos(75+15/2) =
= 2 • sin(60/2) • cos(90/2) =
= 2 • sin(30) • cos(45) =
= 2 • 1/2 • ✓2/2 =
= ✓2/2
c) cos(15) + cos(75) = cos(75) + cos(15) =
= 2 • cos(75+15/2) • cos(75-15) =
= 2 • cos(90/2) • cos(60/2) =
= 2 • cos(45) • cos(30) =
= 2 • ✓2/2• ✓3/2 =
= ✓6/2
d) cos(75) - cos(15) =
= - 2 • sin(75+15/2) • sin(75-15/2) =
= - 2 • sin(90/2) • sin(60/2) =
= - 2 • sin(45) • sin(30) =
= - 2 • ✓2/2• 1/2 =
= - ✓2/2
La fel și la celelalte!
Baftă!!!
