How do you find the EXACT value in simplest radical form for tan (11π/12) by using a sum or difference identity???

1 Answer
Jim G.
Mar 9, 2018

#sqrt3-2#

Explanation:

#"using the "color(blue)"addition formula for tan"#

#•color(white)(x)tan(A+B)=(tanA+tanB)/(1-tanAtanB)#

#(11pi)/12=(2pi)/3+pi/4#

#rArrtan((11pi)/12)=tan((2pi)/3+pi/4)#

#rArrtan((2pi)/3+pi/4)#

#=(tan((2pi)/3)+tan(pi/4))/(1-tan((2pi)/3)tan(pi/4))#

#["note that "tan((2pi)/3)=-tan(pi/3)=-sqrt3]#

#=(-sqrt3+1)/(1+sqrt3)larrcolor(blue)"rationalise the denominator"#

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

#=(1-2sqrt3+3)/(1-3)#

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

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