Question

Stiind ca sin x+ cos x= 3/5, sa se calculeze sin 2x.

Answer 1

Aplicam formula (a+b)^2 si avem:

Stiind ca: $sin^{2} x + cos^{2} x = 1$ si $2sinx*cosx = sin2x$=>

$(sinx+cosx) ^{2} = sin^{2} x + 2sinx*cosx + cos^{2} x \\ 2sinx*cosx = (sinx+cosx) ^{2} - 1 \\ sin2x = (\frac{3}{5})^{2} -1 \\ sin2x = \frac{9}{25} - 1 \\ sin2x = \frac{9}{25} - \frac{25}{25}$

=> $sin2x = - \frac{16}{25}$