Question

Please help me with this problem. I'm kind of stuck and don't know what to do.

Answer 1

Try this option:

1) if csc(u)=9, then 1/sin(u)=9 and sin(u)=1/9;

2) if sin(u)=1/9, then cos(u):

$cos(u)=\sqrt{1-sin^2(u)}=\sqrt{1-\frac{1}{81}}=\frac{4\sqrt{5}}{9};$

3) $if \ sin(u)=\frac{1}{9} \ and \ cos(u)=\frac{4\sqrt{5}}{9}, then$

$sin(2u)=2sin(u)*cos(u)=\frac{8\sqrt{5}}{81};$

$cos(2u)=cos^2(u)-sin^2(u)=\frac{80}{81}-\frac{1}{81}=\frac{79}{81};$

$tan(2u)=\frac{sin(2u)}{cos(2u)}=\frac{\frac{8\sqrt{5}}{81}}{\frac{79}{81} }=\frac{8\sqrt{5}}{79}.$