Jika sin α+sinβ=2√A dan cosα+cosβ=2√B, maka cos (α-β) = ... a. 2A+2B-1 b. [tex] \frac{2A+2B-1}{2} [/tex] c. A+B-2 d. [tex] \frac{A+B-2}{2} [/tex] e. [tex] \fr

rumus cos (a - b) = cos a cos b + sin a sin b

cos a + cos b = 2√B, sin a + sin b = 2√A

(cos a + cos b)^2 = (2√B)^2
(sin a + sin b)^2 = (2√A)^2

cos^2 a + 2 cos cos b + cos^2 b = 4B
sin^2 a + 2 sin a sin b + sin^2 b = 4A
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1 + 2 cos a cos b + 2 sin a sin b + 1 = 4B + 4A
2 + 2 (cos a cos b + sin a sin b) = 4A + 4B
2(cos a cos b + sin a sin b) = 4A + 4B - 2
2 cos (a - b) = 4A + 4B - 2
cos (a - b) = 2A + 2B - 1