Grade 11Trigonometry
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
1 Answer
apurv
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)] .
Other Related Questions on trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
Last Activity: 3 Years ago
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
Last Activity: 4 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
Last Activity: 4 Years ago
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
trigonometry
Last Activity: 4 Years ago