Part a
Remember that
[tex]\sin ^2(\theta)+\cos ^2(\theta)=1[/tex]therefore
[tex]\begin{gathered} \sqrt[]{36\sin^2(\theta)+36\cos^2(\theta)} \\ \sqrt[]{36(\sin^2(\theta)+\cos^2(\theta))} \\ \sqrt[]{36} \\ 6 \end{gathered}[/tex]Part b
Remember that
[tex]\begin{gathered} \tan ^2(\theta)+1=\sec ^2(\theta) \\ \end{gathered}[/tex]substitute in the given expression
[tex]\begin{gathered} \frac{7}{\sec^2(\theta)-\tan^2(\rbrack\theta)} \\ \\ \frac{7}{\tan ^2(\theta)+1-\tan ^2(\theta)} \\ \\ \frac{7}{1}=7 \end{gathered}[/tex]Part c
Substitute the given identities in part a and part b
we have
[tex](1)\cdot(1)=1[/tex]Part d
Remember that
[tex]\csc (\theta)=\frac{1}{\sin (\theta)}[/tex][tex]\sec (\theta)=\frac{1}{\cos (\theta)}[/tex]substitute in the given expression
[tex]\frac{\sin (\theta)}{(\frac{1}{\sin (\theta)})}+\frac{\cos (\theta)}{(\frac{1}{\cos (\theta)})}[/tex][tex]\sin ^2(\theta)+\cos ^2(\theta)=1[/tex]