Question 916481
determine the exact value of tan2x if cotx=4/3,0<x<pi/2?
cotx=1/tanx=4/3
tanx=3/4
{{{tan2x=(2tanx)/(1-tan^2(x))=(2(3/4))/(1-9/16)=(3/2)(7/16)=3/2*16/7=48/14=24/7}}}
..
check:
tanx=3/4
x=36.87
2x=73.74
by calculator:
tan2x=tan 73.74&#730;&#8776;3.4286...
exact value as computed=48/24&#8776;3.4285...