Explain And Answer The Value Of Tan(-105) = ?
1 Answer
May 2, 2018
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