Jika A+B= 1/6π dan cosAcosB = 3/4, maka cos(A-B) = .. a. b. c. d. e.... Question from @WineGinia

October 2018 2 81 Report

Jika A+B= 1/6π dan cosAcosB = 3/4, maka cos(A-B) = ..
a. $\frac{1}{9} + \frac{ \sqrt{3} }{2}$
b. $\frac{3}{2} + \frac{ \sqrt{3} }{2}$
c. $\frac{3}{4} - \frac{ \sqrt{3} }{2}$
d. $\frac{3}{2} - \frac{ \sqrt{3} }{2}$
e. $\frac{ \sqrt{3} }{2}$

alvinteguh A + B = $30\ ^0$
cosA . cos B = 3/4
1/2 (cos (A - B) + cos (A + B) = 3/4
cos (A - B) + cos (A + B) = 3/2
cos (A - B) + cos 30 = 3/2
cos (A - B) + 1/2 √3 = 3/2
cos (A - B ) = (3 - √3) / 2
= $\displaystyle \frac{3}{2} - \frac{ \sqrt{3} }{2}$

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ImmanuelSinaga $\boxed{\text{ Cos (A-B) = Cos A . Cos B + Sin A . Sin B}} \\ \\ \boxed{\text{ Cos (A+B) = Cos A . Cos B - Sin A . Sin B}} \\ \boxed{\text{Cos A . Cos B = }\frac{1}{2}(\text{Cos (a+b)+Cos(a-b)})}} \\ \\ \text{Maka :} \\ \\ \displaystyle\frac{3}{4} \ = \frac{1}{2}(\text{Cos (a+b) + Cos (a-b)}) \\ \\ \frac{3}{4} \ = \frac{1}{2}(\text{Cos (a+b) + Cos (a-b)}) \\ \\ \frac{6}{4} \ = \ \text{Cos 30 + Cos (a-b)} \\ \text{Cos (a-b)} = \ \frac{6}{4}-\frac{1}{2}\sqrt{3} \ = \ \frac{3}{2}-\frac{1}{2}\sqrt{3}===>D.$

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