Jawaban:
[tex] \frac{ \sqrt{6} }{18} [/tex]
Penjelasan dengan langkah-langkah:
[tex] \frac{( \cos(45 {}^{o} )\times \sin(30 {}^{o} ) ) }{ \cos(30 {}^{o} ) + \tan(60 {}^{o} ) } = \\ \\ \frac{( \cos(45 {}^{o} )\times \sin(30 {}^{o} ) ) }{ \frac{ \sqrt{3} }{2} + \tan(60 {}^{o} ) } = \\ \\ \frac{( \cos(45 {}^{o} )\times \sin(30 {}^{o} ) ) }{ \frac{ \sqrt{3} }{2} + \sqrt{3} } = \\ \\ \frac{( \cos(45 {}^{o} )\times \sin(30 {}^{o} ) ) }{ \frac{ \sqrt{3} }{2} + \frac{ \sqrt{3} }{1} } = \\ \\ \frac{( \cos(45 {}^{o} )\times \sin(30 {}^{o} ) ) }{ \frac{ \sqrt{3} }{2} + \frac{2 \sqrt{3} }{ 2\times 1} } = \\ \\ \frac{( \cos(45 {}^{o} )\times \sin(30 {}^{o} ) ) }{ \frac{ \sqrt{3} + 2 \sqrt{3} }{2} } = \\ \\ \frac{( \cos(45 {}^{o} )\times \sin(30 {}^{o} ) ) }{ \frac{ 3\sqrt{3} }{2} } = \\ \\ \cos(45 {}^{o} )\times \sin(30 {}^{o} ) \div \frac{3 \sqrt{3} }{2} = \\ \\ \cos(45 {}^{o} )\times \sin(30 {}^{o} ) \div \frac{2 }{3 \sqrt{3} } = \\ \\ \frac{\cos(45 {}^{o} )\times \sin(30 {}^{o} ) \times 2}{3 \sqrt{3} } = \\ \\ \frac{2\cos(45 {}^{o} )\times \sin(30 {}^{o} )}{3 \sqrt{3} } = \\ \\ \frac{2 \times \frac{ \sqrt{2} }{2} \times \sin(30 {}^{o} ) }{3 \sqrt{3} } = \\ \\ \frac{ \red2 \times \frac{ \sqrt{2} }{ \red2} \times \frac{1}{2} }{3 \sqrt{3} } = \\ \\ \frac{ \frac{ \sqrt{2} \times 1}{2} }{3 \sqrt{3} } = \\ \\ \frac{ \frac{ \sqrt{2} }{2} }{3 \sqrt{3} } = \\ \\ \frac{ \sqrt{2} }{2} \div 3 \sqrt{3 } = \\ \\ \frac{ \sqrt{2} }{2} \times \frac{1}{3 \sqrt{3} } = \\ \\ \frac{ \sqrt{2} \times 1 }{2 \times 3 \sqrt{3} } = \\ \\ \frac{ \sqrt{2} }{6 \sqrt{3} } = \\ \\ \frac{ \sqrt{2} }{6 \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \\ \\ \frac{ \sqrt{6} }{6 \times 3} = \\ \\ \frac{ \sqrt{6} }{18} [/tex]
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