Recall that:
[tex]\begin{gathered} \tan ^2x=\sec ^2x-1, \\ \cot ^2x=\frac{1}{\tan ^2x}\text{.} \end{gathered}[/tex]
Substituting the first identity in:
[tex]\cot ^2x(\sec ^2x-1),[/tex]
we get:
[tex]\cot ^2x\cdot\tan ^2x\text{.}[/tex]
Finally, using the second identity we get:
[tex]\frac{1}{\tan^2x}\tan ^2x=1.[/tex]
Answer:
Statement:
[tex]\cot ^2x(\sec ^2x-1)\text{.}[/tex]
Reason: Given.
Statement:
[tex]=\cot ^2x\cdot\tan ^2x\text{.}[/tex]
Reason: Algebra.
Statement:
[tex]=1.[/tex]
Reason: Reciprocal.
