hendrisyafa
8). sdt A = 180 - sdt B c² = a²+b²- 2ab cos A d² = a²+b²- 2ab Cos B c² + b² = (a²+b²-2ab cos A) + (a²+b²-2ab cos B) = 2a² + 2b² - 2ab (cos A + cos B) = 2a² + 2b² - 2ab ( cos A + Cos (180-A) ) = 2 (a²+ b²) - 2ab ( cos A + cos 180 cos A + sin 180 sin A) = 2 (a² + b²) - 2ab ( cos A + (-1) cos A + 0 sin A) = 2 (a² + b²) - 2ab ( cos A - cos A + 0) = 2 (a² + b²) - 2ab (0) = 2 (a² + b²) - 0 = 2 (a² + b²) terbukti
c² = a²+b²- 2ab cos A
d² = a²+b²- 2ab Cos B
c² + b² = (a²+b²-2ab cos A) + (a²+b²-2ab cos B)
= 2a² + 2b² - 2ab (cos A + cos B)
= 2a² + 2b² - 2ab ( cos A + Cos (180-A) )
= 2 (a²+ b²) - 2ab ( cos A + cos 180 cos A + sin 180 sin A)
= 2 (a² + b²) - 2ab ( cos A + (-1) cos A + 0 sin A)
= 2 (a² + b²) - 2ab ( cos A - cos A + 0)
= 2 (a² + b²) - 2ab (0)
= 2 (a² + b²) - 0
= 2 (a² + b²) terbukti
12). b.c. cos A = b.c.
=
a.c. cos B = a.c.
=
a.b. cos C = a.b.
=
b.c. cos A + a.c. cos B + a.b. cos C = ++
=
= (terbukti)