If ` 2 sin theta = 2 - cos theta` find ` sin theta`

Find (dy)/(dx) if x= 3 cos theta - cos 2theta and y= sin theta - sin 2theta.

Find (dy)/(dx) if x= 3 cos theta - cos 2theta and y= sin theta - sin 2theta.

If x = 2 cos theta - cos 2 theta, y = 2 sin theta - sin 2 theta, find dy/dx at theta = pi/2

If sin theta.cos theta = k then find the sin theta + cos theta .

If (2 sin theta )/(1+ cos theta + sin theta )=x, find the value of (1- cos theta + sin theta )/(1+ sin theta )

(cos theta + sin theta )^(2) + (cos theta - sin theta )^(2) =

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

(cos theta + sin theta) ^ (2) + (cos theta-sin theta) ^ (2) =