Question

Could someone please show me how to solve this

Prove
tan(-theta) = -tan(theta)

Answer 1

take right triangle a,b,c
tan T = a/c first quadrant
tan-T = -a/c fourth quadrant
but
-a/c = -(a/c)

Answer 2

you can also do it by recalling some properties of sin x and cos x:
sin (-x) = -sin x
cos (-x) = cos x
since tan(theta) = (sin(theta))/(cos(theta)),,
tan(-theta) = (sin(-theta))/(cos(-theta))
applying their properties we have:
-(sin(theta))/(cos(theta)) which is equal to -tan(theta)

so there,, =)