Eliminate `theta` between `sin theta + cos theta = x, sin theta - cos theta = y`

Prove that : sin 2 theta= 2sin theta cos theta .

Find sin 2 theta when sin theta + cos theta= 1 .

Eliminate theta between the equation : x =a cos theta + b sin theta, y =a sin theta- b cos theta .

Eliminate theta between the equation : x= h+a cos theta, y=k+ b sin theta .

Eliminate theta between the equation : x = sin theta + cos theta, y = sin theta-cos theta .

The method of eliminating 'theta' from two given equations involving trigonometrical functions of 'theta' . By using given equations involving 'theta' and trigonometrical identities, we shall obtain an equation not involving 'theta' . On the basis of above information answer the following questions. If x sin^(3) theta+ y cos^(3)theta= sin theta cos theta and x sin theta- y cos theta = 0 then (x, y) lie one

If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos theta sin theta , sin^(2) theta , cos theta ],[sin theta ,-cos theta , 0]] ,then f ( pi / 7) is

Find (dy)/(dx) in the following x = e^theta (sin theta + cos theta), y = e^(theta) (sin theta - cos theta)

Find dy/dx , if x and y are connected parametrically by the equations, given below without eliminating the parameter. x cos theta-cos2theta, y = sin theta - sin 2 theta

Prove that all lines represented by the equation (2 cos theta + 3 sin theta ) x + (3 cos theta - 5 sin theta ) y = 5 cos theta - 2 sin theta pass through a fixed point for all theta What are the coordinates of this fixed point ?