3 тригонометрични тъждества

[bombino]

Ако някой може да ми ги реши Благодаряяя мноого!

[dimy93]

2.[tex]\sqrt{2} *(sin\alpha + cos\alpha)=2*(\frac{\sqrt{2}}{2 } sin\alpha +\frac{\sqrt{2}}{2 }cos\alpha)=2*(cos( \frac{\pi }{4} )* sin\alpha +sin( \frac{\pi }{4} )*cos\alpha) = 2*sin(\alpha + \frac{\pi }{4} )[/tex]
3.[tex]sin(\alpha +\beta )*sin(\alpha -\beta )=(sin\alpha *cos\beta +cos\alpha *sin\beta )*(sin\alpha *cos\beta -cos\alpha *sin\beta )=[/tex]
[tex]= sin^{2}\alpha *cos^{2}\beta -cos^{2}\alpha *sin^{2}\beta = sin^{2}\alpha *(1 - sin^{2}\beta ) - sin^{2}\beta *(1 - sin^{2}\alpha ) =[/tex]
[tex]= sin^{2}\alpha - sin^{2}\alpha * sin^{2}\beta - sin^{2}\beta + sin^{2}\alpha * sin^{2}\beta = sin^{2}\alpha - sin^{2}\beta[/tex]