Question

How do you use sum and difference identities to find the exact value of tan(-105)#?

Answer 1

Find value of tan (-105)
Use trig identity:`tan (a + b) = (tan a + tan b)/(1 - tan a.tan b`

Explanation:

On the trig unit circle,

tan (-105) = - tan (105) = - tan (45 + 60)

tan 45 = 1 ; `tan 60 = sqrt3`

`tan (-105) = - ((1 +sqrt3)/(1 - sqrt3))`