diketahui sin alfa=2per3 dan sin beta=√7per4 dengan alfa dan beta sudut lancip.nilai cos alfa+beta adalah

[tex]sin \alpha = \frac{2}{3} [/tex]
[tex] cos^{2} \alpha =1- sin^{2} \alpha [/tex]
[tex] cos^{2} \alpha =1- ( \frac{2}{3} )^{2} = 1 - \frac{4}{9} = \frac{5}{9} [/tex]
[tex]cos \alpha = \frac{ \sqrt{5} }{3} [/tex]

[tex]sin \beta = \frac{ \sqrt{7} }{4} [/tex]
[tex]cos^{2} \beta =1- sin^{2} \beta = 1 - (\frac{ \sqrt{7} }{4}) ^{2} = 1 - \frac{7}{16} [/tex]
[tex]cos \beta = \sqrt{ \frac{9}{16} } = \frac{3}{4} [/tex]

[tex]cos (\alpha + \beta ) = cos \alpha .cos \beta -sin \alpha .sin \beta [/tex]
[tex]cos (\alpha + \beta ) = \frac{ \sqrt{5} }{3} . \frac{3}{4} - \frac{2}{3} . \frac{ \sqrt{7} }{4} = \frac{3 \sqrt{5} -2 \sqrt{7} }{12} [/tex]