Question

Can u please help me solve? I am reviewing for a final, ty

Answer 1

Part A : The students verify the two identity very well and it was properly

solved

`\begin{gathered} sin^2x+cos^2x=1 \\ sin^2x=1-cos^2x \\ cos^2x=1-sin^2x \end{gathered}`

reason why the substitution work for both students

Also the inverse of identity like

`\begin{gathered} (1)/(sinx)=cosecx=cscx \\ (1)/(tanx)=cotx \\ where \\ tanx=(sinx)/(cosx) \\ cotx=(cosx)/(sinx) \end{gathered}`

Therefore the two identity that where used by students A's is

`\begin{gathered} cos^2x=1-sin^2x \\ (1)/(sinx)=cscx \end{gathered}`

The first one appear in Step 3, while the second one appear in Step 5