Answer:
The answer is 2
Step-by-step explanation:
[tex]Cot(x)=\frac{1}{tan(x)} =\frac{Cos(x)}{Sin(x)}[/tex]
[tex]Tan(x) = \frac{Sin(x)}{Cos(x)}[/tex]
[tex]Cos(\frac{\pi }{2} -x)=sin(x)[/tex]
This means that
[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+\frac{\sin \left(\frac{4}{5}\right)}{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}[/tex]
This will be a long one to solve
-> apply cos identity to right side
[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+\frac{\sin \left(\frac{4}{5}\right)}{\cos \left(\frac{\pi }{2}\right)\cos \left(\frac{4}{5}\right)+\sin \left(\frac{\pi }{2}\right)\sin \left(\frac{4}{5}\right)}[/tex]
-> simplify according to unit circle
[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+1[/tex]
->apply cos identity again
[tex]\frac{\cos \left(\frac{\pi }{2}\right)\cos \left(\frac{4}{5}\right)+\sin \left(\frac{\pi }{2}\right)\sin \left(\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+1[/tex]
If you apply for unit circle numbers,
you will get 2
I do not recommend using a calculator for these questions, but instead, turn the form into [tex]sin\frac{\pi }{2}[/tex] other base unit circle locations, and most likely this is the method that your teacher counts as "right."
when using a calculator, it tends to "round" the number, which result in a inaccurate answer
