Solve `4cot2theta=cot^2theta-tan^2theta` – InterviewSolution

InterviewSolution

1.	Solve `4cot2theta=cot^2theta-tan^2theta`
Answer» `4/(tan 2 theta)=1/(tan^(2) theta)-tan^(2) theta` or `(4(1-tan^(2) theta))/(2 tan theta)=(1- tan^(4) theta)/(tan^(2) theta)" "["put "tan 2 theta=(2 tan theta)/(1-tan^(2) theta)]` or `(1-tan^(2) theta)[2 tan theta-(1+tan^(2) theta)]=0` or `(1-tan^(2) theta)(tan^(2) theta-2 tan theta+1)=0` or `(1-tan^(2) theta) (tan theta-1)^(2) =0` or `tan theta= pm 1` `rArr theta= n pi pm pi/4, n in Z`

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