sin 75°=sin(45°+30°)
sin 75°=sin 45°cos 30° + cos 45°sin 30°
[tex] = \frac{ \sqrt{2} }{2} \times \frac{ \sqrt{3} }{2} + \frac{ \sqrt{2} }{2} \times \frac{1}{2} [/tex]
[tex] = \frac{ \sqrt{2} \times \sqrt{3} }{2 \times 2} + \frac{ \sqrt{2} \times 1}{2 \times 2} [/tex]
[tex] = \frac{ \sqrt{6} }{4} + \frac{ \sqrt{2} }{4} [/tex]
[tex] = \frac{ \sqrt{6} + \sqrt{2} }{4} [/tex]
cos 15°=cos(60°-45°)
cos 15°=cos 60°cos 45° + sin 60°sin 45°
[tex] = \frac{1}{2} \times \frac{ \sqrt{2} }{2} + \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{2} }{2} [/tex]
[tex] = \frac{1 \times \sqrt{2} }{2 \times 2} + \frac{ \sqrt{3} \times \sqrt{2} }{2 \times 2} [/tex]
[tex] = \frac{ \sqrt{2} }{4} + \frac{ \sqrt{6} }{4} [/tex]
[tex] = \frac{ \sqrt{6} + \sqrt{2} }{4} [/tex]
[tex] \frac{ \sqrt{6} + \sqrt{2} }{4} - \frac{ \sqrt{6} + \sqrt{2} }{4} = 0[/tex]
sin 75°-cos 15°=0
