`x=e^(theta)(theta+(1)/(theta)),y = e^(-theta)(theta-(1)/(theta))`

Find (dy)/(dx) , when x=e^(theta)(theta+1/theta) and y=e^(-theta)(theta-1/theta)

Find (dy)/(dx),w h e n x=e^(theta)(theta+1/theta)a n dy=e^(-theta)(theta-1/theta)

Find (dy)/(dx), when x=a e^(theta)(sintheta-costheta),y=a e^(theta)(sintheta+costheta)

Assume that lim_(thetararr-1) f(theta) exists and (theta^(2)+theta-2)/(theta+3)le(f(theta))/(theta^(2))le(theta^(2)+2theta-1)/(theta+3) holds for certain interval containing the point theta=-1 " then "lim_(thetararr-1) f(theta)

Integrate the following functions int_(theta_(1))^(theta_(2)) (d theta)/( theta -theta_(0))

y=1/((1+tan theta)^(sin theta-cos theta)+(cot theta)^(cos theta-cot theta))+ 1/((1+tan theta)^(cos theta-sin theta)+(cot theta)^(sin theta-cottheta)) +1/((1+tan theta)^(cos theta-cot theta)+(cot theta)^(cot theta-sin theta)) then (dy)/(dx) at theta=pi/3 is

1/(sec(theta)-tan(theta))+1/(sec(theta)+tan(theta)) =

The normal to the curve x=a(cos theta + theta sin theta), y=a(sin theta - theta cos theta) at any theta is such that

Prove that (sec theta+tan theta -1)/(tan theta -sec theta +1)=cos theta/(1-sin theta)

Prove that (1+sin 2theta)/(1-sin 2theta) = ((1+tan theta)/(1-tan theta))^2