Question

Verify the identity. Step by Step Please. Need Help!!!

cotx/1+cscx=cscx - 1/cotx

Answer 1

like a first step rewrite cot x = cos x/sin x and 1+csc x = ? or csc x -1 = ?

try it in this way ?

Answer 2

\[\cot(x)/1+\csc(x)=\csc(x)-1/\cot(x)\]
\[\cot(x)(\csc(x)-1)/(\csc(x)-1)(\csc(x)+1)\]
\[\sin ^2(x)+\cos^2(x)=1 \]
\[1+\cot ^2(x)=\csc^2(x) \]
\[\csc^2(x)-1=\cot^2(x)\]
\[\cot (x)(\csc(x)-1)/\csc^2(x)-1\]
\[\cot(x)(\csc(x)-1)/\cot ^2(x)\]
\[\csc(x)-1/\cot(x)\]