Question

Помогите плизз
1)5√2sin15π8*cos15π8 2)10√3cosπ3*cos11π6

Answer 1

Синус двойного угла: sin2a = 2sinacosa.

$1)~ 5sqrt{2}sinfrac{15pi}{8}cosfrac{15pi}{8}=frac{5sqrt{2}}{2}sin(2cdotfrac{15pi}{8})=frac{5}{sqrt{2}}sinfrac{15pi}{4}=frac{5}{sqrt{2}}sinfrac{16pi-pi}{4}=\ \ \ =frac{5}{sqrt{2}}sin(4pi-frac{pi}{4})=frac{5}{sqrt{2}}(-sinfrac{pi}{4})=frac{5}{sqrt{2}}cdot(-frac{1}{sqrt{2}})=-frac{5}{2}$

$2)~ 10sqrt{3}cosfrac{pi}{3}cosfrac{11pi}{6}=10sqrt{3}cdotfrac{1}{2}cdot cosfrac{12pi-pi}{6}=5sqrt{3}cos(2pi-frac{pi}{6})=\ \ =5sqrt{3}cdotcosfrac{pi}{6}=5sqrt{3}cdotfrac{sqrt{3}}{2}=frac{15}{2}$