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

1 Answer
Jim G.
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#

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