cos 1/2 A = 3/5--> cos A= 2 cos² 1/2 A -1 cos A = 2 (3/5)² - 1 = 2(9/25) - 1 = 18/25 - 1 = 7/25
sin 1/2 B= 1/2 √3 cos B = 1 - 2 sin² 1/2 B cos B = 1 - 2 (1/2 √ 3)² cos B = 1 - 2(3/4) cos B = 1 - 6/4 = - 2/4 = - 1/2
cos (A + B) + cos (A - B) = 2 cos 1/2(A+B+A-B) cos 1/2 (A+B-A+B) cos(A+B) +cos(A-B) = 2 cos 1/2 (2A) cos 1/2 (2B) cos(A+B) +cos(A-B) = 2 cos A cos B cos(A+B) +cos(A-B) = 2 (7/25). (-1/2) cos (A+B) +cos(A-B) = - 7/25
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Verified answer
Jawabcos 1/2 A = 3/5--> cos A= 2 cos² 1/2 A -1
cos A = 2 (3/5)² - 1 = 2(9/25) - 1 = 18/25 - 1 = 7/25
sin 1/2 B= 1/2 √3
cos B = 1 - 2 sin² 1/2 B
cos B = 1 - 2 (1/2 √ 3)²
cos B = 1 - 2(3/4)
cos B = 1 - 6/4 = - 2/4 = - 1/2
cos (A + B) + cos (A - B) = 2 cos 1/2(A+B+A-B) cos 1/2 (A+B-A+B)
cos(A+B) +cos(A-B) = 2 cos 1/2 (2A) cos 1/2 (2B)
cos(A+B) +cos(A-B) = 2 cos A cos B
cos(A+B) +cos(A-B) = 2 (7/25). (-1/2)
cos (A+B) +cos(A-B) = - 7/25