Question

1. tan a = cot(a + 10°)

Answer 1

Answer:

$a=40+90n$

Step-by-step 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:

$a=40+90n$