Question

Calculati sin 2x,stiind ca x∈(0 si pi supra 2) si cos x=3√5 supra 7.

Answer 1

sin 2x= 2*(sin x)* (cos x)
sin x= radical(1-(cos x)*(cos x) => sin x= radical(1-45/49)= 2/7=>
sin 2x= 2*2/7*3radical(5)/7= 12radical(5)/49

Answer 2

cosx=(3√5)/7 ⇒sinx=$\sqrt{1-cos^2x} = \sqrt{1-\frac{9*5}{49}}= \frac{2}{7}$, sin2x=2sinx*cosx=[2*3(√5)/7]*2/7=$\frac{12 \sqrt{5} }{49}$