тригоном....

[anity123]

някой може ли да реши тази задача --->tg?(45°+?)-1 върху tg?(45°+?)+1 иии пише да се опрости ...

[mathinvalidnik]

[tex]\frac{tg^{2}(45+\alpha)-1}{tg^{2}(45+\alpha)+1 }=\frac{\frac{sin^{2}(45+\alpha)}{cos^{2}(45+\alpha) }-1}{\frac{sin^{2}(45+\alpha)}{cos^{2}(45+\alpha) }+1 }[/tex]=

=[tex]\frac{\frac{sin^{2}(45+\alpha)-cos^{2}(45+\alpha)}{cos^{2}(45+\alpha) }}{\frac{sin^{2}(45+\alpha)+cos^{2}(45+\alpha)}{cos^{2}(45+\alpha) } }=\frac{\frac{sin^{2}(45+\alpha)-cos^{2}(45+\alpha)}{cos^{2}(45+\alpha) }}{\frac{1}{cos^{2}(45+\alpha) } }=sin^{2}(45+\alpha)-cos^{2}(45+\alpha)=\frac{1-cos2(45+\alpha)}{2 }-\frac{(1+cos2(45+\alpha))}{2 }[/tex]

[tex]=-cos(90+2\alpha)=sin2\alpha[/tex]