Question

Help tolong soal sbmptn mat ipa
pilihannya:
a.3/2
b.5/4
c.1
d.1/5
e.1/2 akar3

Answer 1

sin α - sin β =      kedua ruas pangkatkan 2
(sin α - sin β)² = 
sin² α - 2.sin α .sin β + sin² β =   ....pers i
cos α + cos β =   ...kedua ruas pangkathan 2
(cos α + cos β)² = 
cos² α + 2.cos α . cos β + cos² β =   elemenasi dgn pers i
 sin² α -  2.sin α . sin β  + sin² β  = 
----------------------------------------------------------------------------------   +
1 + 2.cos α . cos β - 2.sin α .sinβ + 1 = 1
2.cos α.cos β - 2.sin α  sin β = 1 - 1 - 1
2(cos α. cos β - sin α .sin β) = - 1
cos α .cos β - sin α .sin β = 
cos (α + β) = 
sin² (α + β) + cos² (α + β) = 1
sin² (α + β) +  = 1
sin² (α + β) +  = 1
sin² (α + β) = 1 - 
sin² (α + β) = 
sin (α + β) = 
sin (α + β) = 

Answer 2

SinA-sinB = 3/5
cosA+cosB = 4/5
sin(A+B) = ?

2cos(1/2(A+B))sin(1/2(A-B)) = 3/5
cos(1/2(A+B))sin(1/2(A-B)) = 3/10

2cos(1/2(A+B))cos(1/2(A-B)) = 4/5
cos(1/2(A+B))cos(1/2(A-B)) = 4/10

tan(1/2(A-B)) = 3/4
1/2(A-B) = 37°
A-B = 74°

sin(37) = 3/5
cos(37) = 4/5

cos(1/2(A+B))cos(37) = 4/10
cos(1/2(A+B)) = 4/10 × 5/4 = 1/2
cos(1/2(A+B)) = 1/2
1/2(A+B) = 60°
A+B = 120°

sin(A+B) = sin(120) = sin(180-60)

= sin180cos60 - cos180sin60
= (0 × 1/2) - (-1 × (3)^1/2 /2)
= 1/2 × 3^(1/2)

(( 1/2 akar 3 ))