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Eliminate theta from the equation x=cot theta+cos theta,y=cot theta-cos theta

Eliminate theta from the equation x=cot theta+cos theta,y=cot theta-cos theta
 

Grade:11

1 Answers

apurv
49 Points
3 years ago
 x= cot(theta) + cos(theta) ..... Eqn 1
 y= cot(theta) - cos(theta)..... Eqn 2
Adding 1 and 2 we get cot(theta)= (x+y)/2.....eqn 3
Subtracting 1 and 2 we get cos(theta) = (x-y)/2.....eqn 4
Now as we know cot(theta) = cos(theta)/sin(theta)
From eqn. 3 and 4 we get sin(theta) = (x-y)/(x+y)
Now as we know cos^2(theta) + sin^2(theta) = 1 ...eqn 5
Substituting the values of cos(theta) and sin(theta) in eqn 5 we get sqrt[x^2 + y^2 + 2xy + 4] = 2[(x+y)/(x-y)] .
 

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