Question

найти значение выражения 3sin(2a-п/4)+2cos(3a-п), если a=п/4

Answer 1

$alpha =dfrac{pi}4\\3sin Big(2alpha -dfrac{pi}4Big)+2cosBig(3alpha -piBig)=\\\=3sin Big(dfrac{2pi}4 -dfrac{pi}4Big)+2cosBig(dfrac{3pi}4 -piBig)=\\\=3sin Big(dfrac{pi}4Big)+2cosBig(-dfrac{pi}4Big)=\\\=3 cdotdfrac{sqrt 2}2+2cdotdfrac{sqrt2}2=dfrac{5sqrt2}2=2,5sqrt2$