3sin²x+sin2x=2⇒3sin²x+2sinxcosx-2sin²x-2cos²x=0
sin²x+2sinxcosx-2cos²x=0⇒делим на cos²x:
tg²x+2tgx-2=0;⇒tgx=y;
y²+2y-2=0;⇒y=-1⁺₋√1+2=-1⁺₋√3;
y₁=-1+√3;⇒tgx=-1+√3=0.73;⇒x=arctg0.73+kπ;k∈Z;
y₂=-1-√3;⇒tgx=-1-√3=-2.73;⇒x=arctg(-2.73)+kπ;k∈Z.
Sin(pi/2 - a) =cosa
cos (pi/2 +a) = -sina
tg (3pi/2 - a) = ctga
ctg (pi-a) = -ctga
sin(pi-a) = sina
cos (pi+a)= -cosa
2. sin²γ+sinγ·cosγ·ctgγ=sin²γ+sinγ·cosγ·cosγ/sinγ=sin²γ+cos²γ=1;
3. (sinx-sin³x)/cos²x+2sinx=sinx(1-sin²x)/cos²x+2sinx=
=sinx·cos²x/cos²x +2sinx=sinx+2sinx=3sinx;
4. (5sinφ-3)/(4-5cosφ)-(4+5cosφ)/(3+5sinφ)=
=[(25sin²φ-9)-(16-25cos²φ)]/(4-5cosφ)(3+5sinφ)=
=(25sin²φ-25+25cos²φ)/(4-5cosφ)(3+5sinφ)=
=(25(sin²φ+cos²φ-1)/(4-5cosφ)(3+5sinφ)=0/(4-5cosφ)(3+5sinφ)=0