How do you find the exact functional value tan -105 using the cosine sum or difference identity?

1 Answer
Nghi N.
Sep 25, 2015

Find tan (-105)

Ans: #- (1 + sqrt3)/(1 - sqrt3)#

Explanation:

First find sin (-105) and cos (-105).
sin (-105) = - sin (105) = sin (45 + 60) = sin 45.cos 60 + sin 60.cos 45 =
#= sqrt2/4 + (sqrt2/4)(sqrt3) = - (sqrt2/4)(1 + sqrt3)#
cos (-105) = cos (105) = cos (45 + 60) = cos 45.cos 60 - sin 45.sin 60.
#= (sqrt2/4)(1 - sqrt3)#

#tan (-105) = sin/(cos) = - (1 + sqrt3)/(1 - sqrt3)#
Check by calculator:
tan (-105) = 3.73
#-(1 + sqrt3)/(1 - sqrt3) = - (2.73)/(-0.73) = 3.73. #OK

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