Answer:
[tex]tan(90-{\theta})=1[/tex].
Step-by-step explanation:
In order to find the indicated trigonometric function that is: [tex]tan(90-{\theta})[/tex], we take [tex]sin{\theta}=\frac{3}{\sqrt{13}}[/tex] and [tex]cos{\theta}=\frac{3}{\sqrt{13}}[/tex].
Now, [tex]\frac{sin{\theta}}{cos{\theta}}=\frac{\frac{3}{\sqrt{13}}}{\frac{3}{\sqrt{13}}}[/tex]
⇒[tex]tan{\theta}=1[/tex]
⇒[tex]{\theta}=tan^{-1}(1)[/tex]
⇒[tex]{\theta}=45^{{\circ}}[/tex]
Now, the value of the trigonometric function is given by:
[tex]tan(90-{\theta})=tan(90-45)=cot45=1[/tex]
Thus, [tex]tan(90-{\theta})=1[/tex].
