If `x=2costheta-cos2\ theta` and `y=2sintheta-sin2\ theta` , prove that `(dy)/(dx)=tan((3theta)/2)`

Find (dy)/(dx) : x=2 cos theta- cos^(2) theta and y=2 sin theta- sin 2theta Show that (dy)/(dx)= -1 " when " theta = (pi)/(2)

If x = a cos theta + b sin theta and y =asin theta-b cos theta , then prove that y^2 (d^2y)/(dx^2)-x(dy)/(dx)+y=0

If tan theta +sin theta = p and tan theta-sin theta = q , prove that p^(2)-q^(2)=4sqrt(pq)

If x +y= 3-cos4theta and x-y=4sin2theta then

If x sin^(3)theta + y cos^(3)theta = sintheta costheta and x sin theta = y cos theta , prove that x^(2) + y^(2) = 1.

If sintheta + sin^(2)theta = 1 , prove that cos^(2)theta + cos^(4)theta = 1

If sintheta+costheta=1 , then the value of sin(2theta) is

By using above basic addition/ subtraction formulae, prove that (i) tan (A+B)=(tan A+tan B)/(1-tan A tan B) , (ii) tan (A-B)=(tan A-tanB)/(1+tan A tan B) (iii) sin2theta=2sintheta costheta , (iv) cos2theta=cos^(2)theta=1-2sin^(2)theta=2cos^(2)theta-1 (v) tan 2theta=(2 tan theta)/(1-tan^(2) theta)

Prove : (2 sin theta cos theta-cos theta)/(1-sin theta+sin^(2) theta-cos^(2) theta)=cot theta

If cos theta + sin theta = p and sec theta + cosec theta = q , prove that q (p^(2) - 1) = 2p .