Question

Cos4xcosx-sin4xsinx=(минус) корень из 2/2

Answer 1

$cos4xcosx-sin4xsinx=- \frac{ \sqrt{2} }{2} \\ \frac{cos(4x-x)+cos(4x+x)-cos(4x-x)+cos(4x+x)}{2} =- \frac{ \sqrt{2} }{2} \\ \frac{cos3x+cos5x-cos3x+cos5x}{2} = - \frac{ \sqrt{2} }{2} \\ cos5x=- \frac{ \sqrt{2} }{2} \\ \left \{ {{5x= \frac{3 \pi }{4}+2 \pi n } \atop {5x= \frac{5 \pi }{4}+2 \pi n }} \right. \\ \left \{ {{x= \frac{3 \pi }{20}+ \frac{2 \pi n}{5} } \atop {x= \frac{ \pi }{4}+ \frac{2 \pi n}{5} }} \right. \\ OTBET: \frac{ \pi }{4}+ \frac{2 \pi n}{5} ; \frac{3 \pi }{20}+ \frac{2 \pi n}{5}$ n∈Z