If tan alpha=x+1 & tan bita=x-1 Then find what is 2cot(alpha-bita)=?

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Answer 1 · 2018-05-13T16:16:22

#rarr2cot(alpha-beta)=x^2#

Given that, #tanalpha=x+1 and tanbeta=x-1#.

#rarr2cot(alpha-beta)#

#=2/(tan(alpha-beta))=2/((tanalpha-tanbeta)/(1+tanalpha*tanbeta))=2[(1+tanalphatanbeta)/(tanalpha-tanbeta)]#

#=2[(1+(x+1)*(x-1))/((x+1)-(x-1))]#

#=2[(cancel(1)+x^2cancel(-1))/(cancel(x)+1cancel(-x)+1]]=2[x^2/2]=x^2#

Answer 2 · 2018-05-13T16:22:47

#2cot(alpha-beta)=x^2#

We have #tanalpha=x+1# and #tanbeta=x-1#

As #tan(alpha-beta)=(tanalpha-tanbeta)/(1+tanalphatanbeta)#

#2cot(alpha-beta)=2/tan(alpha-beta)=2[(1+tanalphatanbeta)/(tanalpha-tanbeta)]#

= #2[(1+(x+1)(x-1))/(x+1-(x-1))]#

= #2*(1+x^2-1)/(x+1-x+1)#

= #(2x^2)/2=x^2#