Question 973679
2 csc(2x) tan(x) = sec^2(x) 
start with left side:
{{{2csc(2x)tan(x)=2*(1/sin(2x))tan(x)=2/(2sin(x)cos(x))(sin(x)/cos(x))=(1/cos^2(x))=sec^2(x)}}}
verified: left side=right side
and 
csc(x) = [cot(x)]/[cos(x)]
start with right side:
{{{cot(x)/cos(x)=(cos(x)/sin(x))/(cos(x))=(1/sin(x))=csc(x)}}}
verified: right side = left side