Answer:
[tex]a=40+90n[/tex]
Step-by-step explanation:
Use a cofunction identity on the right hand side or left hand side...
So [tex]\tan(a)=\cot(90-a)[/tex].
We have the equation:
[tex]\tan(a)=\cot(a+10)[/tex]
Make the above replacement:
[tex]\cot(90-a)=\cot(a+10)[/tex]
Since cotangent has period 180 degrees, we can also write this as:
[tex]\cot(90-a+180n)=\cot(a+10)[/tex]
So solving the following will give us a set of solutions for [tex]a[/tex]:
[tex]90-a+180n=a+10[/tex]
Add [tex]a[/tex] on both sides:
[tex]90+180n=2a+10[/tex]
Subtract 10 on both sides:
[tex]80+180n=2a[/tex]
Divide both sides by 2:
[tex]40+90n=a[/tex]
Symmetric property:
[tex]a=40+90n[/tex]
