Question

X= cot theta + cos theta and y = cot theta - cos theta then eliminate theta

Answer 1

Given : x = cot theta + cos theta and y = cot theta - cos theta

To find: Eliminate theta.

Solution:

• Now we have given the value of x and y as:

                    x = cot theta + cos theta  ................(i)

                    y = cot theta - cos theta    ...............(ii)

• Now adding i and ii, we get:

                    x + y = cot theta + cos theta + cot theta - cos theta

                    x + y = 2 cot theta

                    x + y = 2/tan theta

                    tan theta = 2 / x+y

• Now subtracting ii from i, we get:

                    x - y = cot theta + cos theta - cot theta + cos theta

                    x - y = 2 cos theta

                    x - y = 2 / sec theta

                    sec theta = 2 / x - y

• Now we know that 1 + tan^2 theta = sec^ theta

• So putting the values in formula, we get:

                    1 + (2 / x+y)^2 = (2 / x - y)^2

Answer:

           So after eliminating theta, we get:  1 + (2 / x+y)^2 = (2 / x - y)^2