How do you find the EXACT value in simplest radical form for tan (11π/12) by using a sum or difference identity???
1 Answer
Mar 9, 2018
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#