Question

How do you simplify tan(-35 deg) using trigonometric identities?

the answer works out to be cot(125 deg) but I do not know why.

Answer 1

Please see below.

Explanation:

.

`tan(-35^@)=sin(-35^@)/cos(-35^@)`

We know:

`sin(pi/2-theta)=costheta`

`cos(pi/2-theta)=sintheta`

In our problem, `theta=-35^@`

Let's plug it in:

`tan(-35^@)=cos(90^@-(-35^@))/sin(90^@-(-35^@))=cos125^@/(sin125^@)=cot125^@`