Question

Bila A + B = 270 , maka cos A + cos B sama dengan...
a. sin A . Sin B
b. sin 2B
c. sin A + sin B
d. 2 cos B
e. cos 2B

Answer 1

Verified answer

Bab Trigonometri
Matematika SMA Kelas X

A + B = 270°

A = 270° - B

A - B = 270° - B - B = 270° - 2B

cos A + cos B = 2 . cos ((A + B)/2) . cos ((A - B)/2)
cos A + cos B = 2 . cos (270°/2) . cos ((270° - 2B)/2)
cos A + cos B = 2 . cos 135° . cos (135° - B)
cos A + cos B = 2 . (-1/2 √2) . (cos 135° cos B + sin 135° . sin B)
cos A + cos B = -√2 . (-1/2 √2 . cos B + 1/2√2 . sin B)
cos A + cos B = cos B - sin B 

A + B = 270°
B = 270° - A
cos B = cos (270° - A)
cos B = cos 270° . cos A + sin 270° . sin A
cos B = 0 + (-1) , sin A
cos B = - sin A

sin B = sin (270° - A)
sin B = sin 270° . cos A - cos 270° . sin A
sin B = (-1) . cos A - 0
sin B = - cos A

cos A + cos B = - sin A - sin B
atau
cos A + cos B = cos A - (- cos A)
cos A + cos B = 2 cos A