Nilai dari sin 75° dan cos 105°

[tex]rumus \\ \sin( \alpha + \beta ) = \sin( \alpha ) cos( \beta ) + \sin( \beta ) \cos( \alpha) \\ \cos( \alpha + \beta ) = \sin( \alpha ) \sin( \beta ) - \cos( \alpha ) \cos( \beta ) \\ \\ \sin(75) = \sin(45 + 30) ... \\ = \sin(45) \cos(30) + \sin(30) \cos(45) \\ = \frac{1}{2} \sqrt{2} \times \frac{1}{2} \sqrt{3} + \frac{1}{2} \times \frac{1}{2} \sqrt{2} \\ \\ = \frac{1}{4} \sqrt{6} + \frac{1}{4} \sqrt{2} \\ \\ = \frac{1}{4} ( \sqrt{6} + \sqrt{2} ) \\ \\ \cos(105 ) = \cos(60 + 45) \\ = \sin(60) \sin(45) - \cos(60) cos(45) \\ = \frac{1}{2} \sqrt{3} \times \frac{1}{2} \sqrt{2} - \frac{1}{2} \times \frac{1}{2} \sqrt{2} \\ \\ = \frac{1}{4} \sqrt{6} - \frac{1}{4} \sqrt{2} \\ \\ = \frac{1}{4} ( \sqrt{6} - \sqrt{2} )[/tex]