Solution
Part A : The students verify the two identity very well and it was properly
solved
[tex]\begin{gathered} sin^2x+cos^2x=1 \\ sin^2x=1-cos^2x \\ cos^2x=1-sin^2x \end{gathered}[/tex]
reason why the substitution work for both students
Also the inverse of identity like
[tex]\begin{gathered} \frac{1}{sinx}=cosecx=cscx \\ \frac{1}{tanx}=cotx \\ where \\ tanx=\frac{sinx}{cosx} \\ cotx=\frac{cosx}{sinx} \end{gathered}[/tex]
Therefore the two identity that where used by students A's is
[tex]\begin{gathered} cos^2x=1-sin^2x \\ \frac{1}{sinx}=cscx \end{gathered}[/tex]
The first one appear in Step 3, while the second one appear in Step 5
