Question

How do you find the exact functional value tan 345 using the cosine sum or difference identity?

Answer 1

Find tan 345 by the cosine sum or difference identity.

Ans:`(sqrt6 - sqrt2)/(sqrt6 + sqrt2)`

Explanation:

tan 345 = tan (165 + 180) = tan (165) = - tan 15 deg
sin 15 = sin (45 - 30) = sin 45.cos 30 - sin 30.cos 45 =

`= ((sqrt3)/2)((sqrt2)/2) - (1/2)(sqrt2/2) = (sqrt6 - sqrt2)/4`

cos 15 = cos (45 - 30) = cos 45.cos 30 + sin 45.sin 30 =

`= (sqrt2/2)(sqrt3/2) + (sqrt2/2)(1/2) = (sqrt6 + sqrt2)/4`

`tan 345 = - tan 15 = - sin 15/cos 15 = - (sqrt6 - sqrt2)/(sqrt6 + sqrt2)`