Question

I need the statements and rules Rules ( Algebra, quotient, reciprocal etc

Answer 1

Recall that:

`\begin{gathered} \tan ^2x=\sec ^2x-1, \\ \cot ^2x=(1)/(\tan ^2x)\text{.} \end{gathered}`

Substituting the first identity in:

`\cot ^2x(\sec ^2x-1),`

we get:

`\cot ^2x\cdot\tan ^2x\text{.}`

Finally, using the second identity we get:

`(1)/(\tan^2x)\tan ^2x=1.`

Answer:

Statement:

`\cot ^2x(\sec ^2x-1)\text{.}`

Reason: Given.

Statement:

`=\cot ^2x\cdot\tan ^2x\text{.}`

Reason: Algebra.

Statement:

`=1.`

Reason: Reciprocal.