Question

Решить нужно , буду ) cos7x*sinx-sin7x*cosx=0.5

Answer 1

$cos7x*sinx-sin7x*cosx=0.5$

$sin(x-7x)=0.5$

$sin(-6x)=0.5$

$sin6x=-0.5$

$6x=(-1)^k arcsin(-0.5)+ \pi k,$ $k$ ∈ $Z$

$6x=(-1)^{k+1} arcsin0.5+ \pi k,$ $k$ ∈ $Z$

$6x=(-1)^{k+1} \frac{ \pi }{6} + \pi k,$ $k$ ∈ $Z$

$x=(-1)^{k+1} \frac{ \pi }{36} + \frac{\pi k}{6} ,$ $k$ ∈ $Z$

P.S.
$sin(x-y)=sinxcosy-sinycosx$

Answer 2

1/2 (sin(7x+x)+sin(x-7x))-1/2(sin(7x+x)+sin(7x-x))=0.5
1/2 sin8x + 1/2sin(-6x) - 1/2 sin8x- 1/2 sin6x=0.5
-1/2 sin6x - 1/2 sin6x=0.5
-sin6x=0.5
Sin6x=0.5
6x=(-1)^n arcsin(0.5) + PIn
6x=(-1)^n PI/6 + PIn
X=(-1)^n PI/36 + PIn