Find sin 2x, cos 2x, and tan 2x if sin x= 3/square root 10

Step-by-step explanation:

sin2x=2sinxcosx=2*3/√10*1/√10=6/10=3/5

cos2x=cos^2x-sin^2x=1/10-9/10=-8/10=-4/5

tan2x=sin2x/cos2x=3/-4=-3/4

..

Check:

sinx=3/√10

x=71.565

2x=143.13

sin2x=sin(143.13)=0.6000

exact value as computed=3/5=0.6000

cos2x=cos(143.13)≈.0.7999

exact value as computed=4/5=0.8000

tan2x=tan(143.13)≈-0.7500

exact value as computed=-3/4=-0.7500