Nilai daei sin 30 + cos 315 / tg 45 - cos 224 adalah */ artinya per

[tex] \sin(30) = \frac{1}{2} \\ \cos(315) = \cos(360 - 45) \\ = \cos(45) \\ = \frac{1}{2} \sqrt{2} \\ = \frac{ \sqrt{2} }{2} \\ \tan(45) = 1 \\ \cos(225) = \cos(180 + 45) \\ = \cos(45) \\ = \frac{1}{2} \sqrt{2} \\ = \frac{ \sqrt{2} }{2} [/tex]
[tex] \frac{ \sin(30) + \cos(315) }{ \tan(45) - \cos(225) } \\ = \frac{ \frac{1}{2} + \frac{ \sqrt{2} }{2} }{1 - \frac{ \sqrt{2} }{2} } \\ = \frac{ \frac{1 + \sqrt{2} }{2} }{ \frac{2}{2} - \frac{ \sqrt{2} }{2} } \\ = \frac{ \frac{1 + \sqrt{2} }{2} }{ \frac{2 - \sqrt{2} }{2} } \\ = \frac{1 + \sqrt{2} }{2} \times \frac{2}{2 - \sqrt{2} } \\ = \frac{1 + \sqrt{2} }{2 - \sqrt{2} } \\ = \frac{1 + \sqrt{2} }{2 - \sqrt{2} } \times \frac{2 + \sqrt{2} }{2 + \sqrt{2} } \\ = \frac{2 + \sqrt{2} + 2 \sqrt{2} + \sqrt{4} }{4 + 2 \sqrt{2} - 2 \sqrt{2} - \sqrt{4} } \\ = \frac{2 + 3 \sqrt{2} + 2 }{4 - 2} \\ = \frac{4 + 3 \sqrt{2} }{2} [/tex]

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