1д

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Опростете изразите
а)1-2sin²[tex]\alpha[/tex]+cos2[tex]\alpha[/tex]
б)[tex]\frac{2tg15°}{1-tg²15°}[/tex]
в)(sin²[tex]\alpha[/tex]-2sin[tex]\alpha[/tex]cos[tex]\alpha[/tex]-cos²[tex]\alpha[/tex])²
г)cos4[tex]\alpha[/tex]+2sin²2[tex]\alpha[/tex]

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а)
[tex]1-2sin²\alpha+cos2\alpha=\cancel {sin ^2 \alpha} + cos ^2 \alpha-2sin^2 \alpha+cos^2\alpha\cancel {- sin^2 \alpha}=2(cos^2 \alpha - sin ^2 \alpha)=2 cos 2 \alpha[/tex]
б)
[tex]\frac{2tg15°}{1-tg²15°} = tg 30 ^\circ = \frac {\sqrt{3}}{3}[/tex]
в)
[tex](sin^2 \alpha-2sin\alpha cos\alpha-cos^2\alpha)^2 =(-sin 2 \alpha -cos2 \alpha )^2=(sin 2 \alpha +cos2 \alpha )^2= sin^2 2 \alpha + cos ^2 2\alpha+ 2 sin 2 \alpha cos 2 \alpha=1+sin4 \alpha[/tex]
г)
[tex]cos4\alpha+2sin^2 2\alpha= cos^2 2 \alpha - sin^2 2 \alpha + 2 sin ^2 2 \alpha= cos^2 2 \alpha + sin^2 2 \alpha =1[/tex]