Question

If tanx=1/root7 then cosec^2

Answer 1

$tanx= \frac{1}{ \sqrt{7} } \\cotx= \frac{1}{tanx}= \sqrt{7} \\\ \\we\ know\ that\ \\cosec^2x-cot^2x=1\\ \Rightarrow cosec^2x-( \sqrt{7} )^2=1\\ \Rightarrow cosec^2x-7=1\\ \Rightarrow cosec^2x=1+7\\ \Rightarrow cosec^2x=\boxed8$