[tex]csc2x-cot2x=tanx \\ \\ (\frac{1}{2}cscxsecx) -( \frac{cotx-tanx}{2} )=tanx \\ \\ (\frac{cscxsecx}{2}) -( \frac{cotx-tanx}{2} )=tanx \\ \\ (\frac{ \frac{1}{sinx} \frac{1}{cosx} }{2}) -( \frac{cotx-tanx}{2} )=tanx \\ \\ (\frac{1}{2(sinxcosx)}) -( \frac{cotx-tanx}{2} )=tanx \\ \\ (\frac{1}{2(sinxcosx)}) -( \frac{(sinxcosx)*cotx-tanx}{2*(sinxcosx)} )=tanx \\ \\ \frac{1-(cos^2x-sin^2x)}{2(sinxcosx)} =tanx \\ \\ \frac{1-cos^2+sin^2x}{2(sinxcosx)}=tanx [/tex]
[tex]\frac{sin^2x+sin^2x}{2(sinxcosx)} =tanx \\ \\ \frac{1-cos2x}{sin2x} =tanx \\ \\ \frac{sin2x}{cos2x+1}=tanx \\ \\ tanx=tanx [/tex]
