Question

Помогите решить $cos^215*cos^2 75$

Answer 1

$cos^{2}15^{circ} cdot cos^{2}75^{circ} = (cos 15^{circ} cdot cos 75^{circ})^{2} = left(dfrac{1}{2} left(cos (15^{circ} -75^{circ}) + cos(15^{circ} + 75^{circ}) right) right)^{2} =\= left(dfrac{1}{2}(cos 60^{circ} + cos 90^{circ}) right)^{2} = left(dfrac{1}{2}left(dfrac{1}{2} + 0 right) right)^{2} = left(dfrac{1}{4} right)^{2} = dfrac{1}{16}$

Ответ: $dfrac{1}{16}$

Воспользуйтесь формулами:

$a^{n} cdot b^{n} = (ab)^{n}$

$cos alpha cos beta = dfrac{1}{2} (cos(alpha - beta ) + cos (alpha + beta ))$

$cos alpha = cos (-alpha)$ — функция косинус четная.