Question

sinp/4*cosp/4-sinp/4*cosp/6
(cos75⁰-sin75⁰)^2

нужно все расписать и решить ​

Answer 1

Ответ:

$\bf3) \frac{1}{2} - \frac{ \sqrt{6} }{4} \\ \bf4) \frac{1}{2}$

Объяснение:

$3)\displaystyle \sin \frac{\pi}{4}\cdot \cos\frac{\pi}{4} - \sin \frac{\pi}{4} \cdot \cos \frac{\pi}{6} = \frac{ \sqrt{2} }{2} \cdot \frac{ \sqrt{2} }{2} - \frac{ \sqrt{2} }{2} \cdot \frac{ \sqrt{3} }{2} = \frac{2}{4} - \frac{ \sqrt{6} }{4} = \bf \frac{1}{2} - \frac{ \sqrt{6} }{4}$

$4) \underbrace{ ( \cos75 {}^{\circ } - \sin75 {}^{ \circ}) {}^{2} }_{ _{\bf(a - b) ^{2} = a ^{2} - 2ab + b ^{2} } } = \cos {}^{2} 75 ^{\circ} - 2 \cos75 ^{\circ} \sin75 {}^{\circ} + \sin {}^{2} 75 ^{\circ} = 1 - \sin(2 \cdot75 {}^{\circ} ) = 1 - \sin150 {}^{\circ} = 1 - \frac{1}{2} = \bf \frac{1}{2}$