Question

sinx , cosx scris in functie de tg$\frac{x}{2}$ , notata eventual cu un t

Answer 1

Răspuns

Asta ar fi o idee.

Explicație pas cu pas:

$tg \frac{x}{2} = \frac{sin\frac{x}{2} }{cos\frac{x}{2}}$

$sinx=2sin\frac{x}{2}cos\frac{x}{2}=2 tg\frac{x}{2}cos^2\frac{x}{2}$

$cosx= 1- sin^2\frac{x}{2} = 1-(tg\frac{x}{2}cos\frac{x}{2} )^2$

Answer 2

$\it sinx=\dfrac{2t}{1+t^2}\\ \\ \\ cosx=\dfrac{1-t^2}{1+t^2}$