Explain And Answer The Value Of Tan(-105) = ?

1 Answer
May 2, 2018

2+sqrt3

Explanation:

"using the "color(blue)"trigonometric identities"

•color(white)(x)tan(-x)=-tanx

•color(white)(x)tan(x+y)=(tanx+tany)/(1-tanxtany)

rArrtan(-105)=-tan(105)

"we can express "105=60+45

rArrtan(105)=tan(60+45)

=(tan60+tan45)/(1-tan60tan45)

=(1+sqrt3)/(1-sqrt3)

"multiply numerator/denominator by "(1+sqrt3)

=((1+sqrt3)(1+sqrt3))/((1-sqrt3)(1+sqrt3))

=(4+2sqrt3)/(-2)=-2-sqrt3

rArrtan(-105)=-(-2-sqrt3)=2+sqrt3