Question

Diketahui a+b+c = 180 derajat , cos (a+c) cos b = -1/2 maka cos (a-b+c)=

Answer 1

Penjelasan dengan langkah-langkah:

a + b + c = 180º

(a + c) = 180 - b

cos(a + c)cosb = - 1/2

cos(180 - b)cosb = -1/2

-cosb.cosb = -1/2

cos²b = 1/2..............(1)

sin²b = 1 - cos²b

sin²b = 1- 1/2

sin²b = 2/2 - 1/2

sin²b = 1/2...............(2)

cos(a - b + c)

= cos(a + c - b)

= cos[(180 - b) - b]

= cos(180 - 2b).........dikuadran 2

= -cos2b

= -[cos²b - sin²b]

= -[ 1/2 - 1/2 ]

= 0

jadi : cos (a + c - b ) = 0

Answer 2

Penjelasan dengan langkah-langkah:

menggunakan rumus :

2 cos A cos B = cos (A+B) + cos (A-B) maka :

cos (a + c) cos b = -1/2

--------------------------------- x 2

2 cos (a + c) cos b = -1

cos ((a + c) + b) + cos ((a + c) - b) = -1

cos (a + c + b) + cos (a + c - b) = -1

penulisan a, b, dan c nya diurutkan menjadi :

cos (a + b + c) + cos (a - b + c) = -1

karena a + b + c = 180° maka

cos (a + b + c) = cos 180° sehingga

cos (a + b + c) + cos (a - b + c) = -1

cos 180° + cos (a - b + c) = -1

cos 180° = -1 maka

-1 + cos (a - b + c) = -1

------------------------------------- + 1

-1 + 1 + cos (a - b + c) = -1 + 1

cos (a - b + c) = 0

semoga membantu.