Diketahui cos (A+B)= 1/2, sin (A-B) =1/2, A dan B sudut lancip. Tentukan nilai sin^2 A+ cos^2 B Bantu dong pliiss:

jawab


cos (a+b) = 1/2  = cos 60
a + b = 60

sin (a - b) = 1/2 = sin 30
a - b = 30

a + b = 60
a - b = 30
2a=90
a = 45

a+ b = 60
45+ b = 60
b = 15

cos 15 = cos (45-30)
= cos 45 cos 30 + sin 45 sin 30
= 1/2 √2 . 1/2 √3 + 1/2√2.1/2
= 1/4 √6 + 1/4 √2
= 1/4 (√6 + √2)

cos² 15 = (1/4)² (√6 + √2)² = 1/16 (8 + 4√3)
cos² 15 = 1/2 + 1/4 √3

sin ² A+ cos² B = ( sin 45)² + (cos B)²
= (1/2 √2)² + (1/4 (√6 + √2)²
= 1/2  + 1/2 - 1/4 √3
= 1 - 1/4 √3
= 1/4 ( 4 - √3)