Question

1. tan a = cot(a + 10°)

Answer 1

`a=40+90n`

Explanation:

Use a cofunction identity on the right hand side or left hand side...

So
`\tan(a)=\cot(90-a)`.

We have the equation:

`\tan(a)=\cot(a+10)`

Make the above replacement:

`\cot(90-a)=\cot(a+10)`

Since cotangent has period 180 degrees, we can also write this as:

`\cot(90-a+180n)=\cot(a+10)`

So solving the following will give us a set of solutions for
`a`:

`90-a+180n=a+10`

Add
`a` on both sides:

`90+180n=2a+10`

Subtract 10 on both sides:

`80+180n=2a`

Divide both sides by 2:

`40+90n=a`

Symmetric property:

`a=40+90n`