Question

sin 75° вычислите
cos 15°

Answer 1

$cos15 = cos\dfrac{30}{2} = \sqrt{\dfrac{1 + cos30}{2}} = \sqrt{\dfrac{1 + \dfrac{\sqrt{3} }{2} }{2} } = \sqrt{\dfrac{1 + \sqrt{3} }{4}}  = \dfrac{\sqrt{1 + \sqrt{3} } }{2}$

$sin75 = cos(90 - 75) = cos15$

Ответ: sin75° = cos15° = √(1 + √3)/2