Помогите решить 1)1-(cos²[latex] \alpha [/latex] - sin²[latex] \alpha [/latex] ) =? 2)1-sin[latex] \alpha [/latex]cos[latex] \alpha [/latex]tg[latex] \alpha [/latex] =? 3) cos²[latex] \alpha [/latex]tg²[latex] \alpha [/latex] +...

[latex]1)1-(cos^2 \alpha - sin^2 \alpha ) =cos^ \alpha +sin^2 \alpha -cos^2 \alpha +sin^2 \alpha =2sin^2 \alpha [/latex] [latex]2)1-sin \alpha\cdot cos \alpha \cdot tg \alpha =1-sin \alpha \cdot cos \alpha \cdot \frac{sin \alpha }{cos \alpha }=1-sin^2 \alpha =cos^2 \alpha [/latex] [latex]3) cos^2\alpha\cdot tg^2 \alpha + 5cos^2 \alpha - 1= \\ \\=cos^2\alpha\cdot \frac{sin^2 \alpha}{cos^2 \alpha} + 5cos^2 \alpha - 1=sin \alpha ^{2}+cos^2 \alpha +4cos^2 \alpha -1=\\ \\==1+4cos^2 \alpha-1=4cos^2 \alpha [/latex] [latex]4) sin \alpha + 3sin^2 \alpha+3cos^2 \alpha =sin \alpha +3(sin^2 \alpha +cos^2 \alpha )=sin \alpha +3\cdot1= \\ \\ =sin \alpha +1[/latex]