Question

Find the value of ?

tan `theta` + cot `theta` = 2 then find (tan `theta` - cot `theta`)

Answer 1

`0`

Explanation:

We have:

`sintheta/costheta + costheta/sintheta = 2`

`(sin^2theta + cos^2theta)/(costhetasintheta) = 2`

`1 = 2costhetasintheta`

`1 = sin(2theta)`

This means that

`arcsin(1) = 2theta`

`pi/2 = 2theta`

`theta = pi/4`

Now we have:

`tan(pi/4) - cot(pi/4) = 1 - 1 = 0`

Hopefully this helps!