tan x + sin x = 2 tan x sin x s i n x c o s x + s i n x = s i n x c o s x ∗ s i n x s i n x + s i n x ∗ c o s x = 2 sin 2 x s i n x + s i n x ∗ c o s x − 2 sin 2 x = 0 s i n x ( 1 + c o s x − 2 sin x ) = 0 {\displaystyle {\begin{aligned}&\tan {x}+\sin {x}=2\tan {x}\sin {x}\\&{\frac {sinx}{cosx}}+sinx={\frac {sinx}{cosx}}*sinx\\&sinx+sinx*cosx=2\sin ^{2}x\\&sinx+sinx*cosx-2\sin ^{2}x=0\\&sinx(1+cosx-2\sin x)=0\\\end{aligned}}}
1 + c o s x − 2 sin 2 x = 0 / − 1 − 2 sin 2 x + c o s x = − 1 / : ( − 1 ) 2 sin 2 x − c o s x = 1 / : a = 2 sin x − 1 2 ∗ c o s x = 1 2 { tan − 1 = a b tan − 1 = 1 2 α = 26.56 sin x − tan 26.56 ∗ c o s x = 1 2 sin x − s i n 26.56 cos 26.56 ∗ c o s x = 1 2 / ∗ c o s 26.56 cos 26.56 ∗ sin x − sin 26.56 ∗ c o s x = 1 2 ∗ cos 26.56 { sin ( α ± β ) = sin α ∗ cos β ± cos α ∗ sin β 1 2 ∗ cos 26.56 = 0.45 s i n ( x − 26.56 ) = 0.45 s i n − 1 0.45 ⇒ s i n 26.74 s i n ( x − 26.56 ) = s i n 26.74 / : s i n x − 26.56 = 26.74 { x 2 − 26.56 = 26.74 + 360 k x 2 = 56.12 + 360 k x 3 − 26.56 = ( 180 − 26.56 ) + 360 k x 3 = 126.88 + 360 k {\displaystyle {\begin{aligned}&1+cosx-2\sin ^{2}x=0/-1\\&-2\sin ^{2}x+cosx=-1/:(-1)\\&2\sin ^{2}x-cosx=1/:a=2\\&\sin x-{\frac {1}{2}}*cosx={\frac {1}{2}}\\&{\begin{cases}\tan ^{-1}={\frac {a}{b}}\\\tan ^{-1}={\frac {1}{2}}\\\alpha =26.56\end{cases}}\\&\sin x-\tan {26.56}*cosx={\frac {1}{2}}\\&\sin x-{\frac {sin{26.56}}{\cos {26.56}}}*cosx={\frac {1}{2}}/*cos{26.56}\\&\cos {26.56}*\sin x{\color {red}-}\sin {26.56}*cosx={\frac {1}{2}}*\cos {26.56}\\&{\begin{cases}\color {blue}\color {blue}\sin(\alpha \pm \beta )=\sin \alpha *\cos \beta \pm \cos \alpha *\sin \beta \\\color {blue}{\frac {1}{2}}*\cos {26.56}=0.45\end{cases}}\\&sin({x-26.56})=0.45\\&\color {blue}sin^{-1}0.45\Rightarrow sin{26.74}\\&sin({x-26.56})=sin{26.74}/:sin\\&x-26.56=26.74\\&{\begin{cases}x_{2}-26.56=26.74+360k\\x_{2}=56.12+360k\\x_{3}-26.56=(180-26.56)+360k\\x_{3}=126.88+360k\end{cases}}\\\end{aligned}}}
sin x = 0 x 1 = 180 k {\displaystyle {\begin{aligned}&\sin x=0\\&x_{1}=180k\end{aligned}}}
