`sin(30^(@)+theta)=(1)/(2)(costheta+sqrt(3)sintheta)`.

The parametric representation of a point on the ellipse whose foci are (3,0) and (-1,0) and eccentricity 2//3 , is a) (1+3costheta,sqrt(3)sintheta) b) (1+3costheta,5sintheta) c) (1+3costheta,1+sqrt(5)sintheta) d) (1+3costheta,sqrt(5)sintheta)

Prove the following (sin theta) /(1+costheta) =(1-costheta) /(sintheta)

If int(sintheta-costheta)/((sintheta+costheta)sqrt(sinthetacostheta+sin^(2)thetacos^(2)theta))d theta = "cosec"^(_1)(f(theta))+C , then

int((sintheta+costheta))/sqrt(sin2theta)"d"theta=

int((sintheta+costheta))/sqrt(sin2theta)"d"theta=

If sintheta -cos theta=sqrt(2)costheta,"show that" sintheta+costheta=sqrt(2)sintheta(0ltthetalt pi/2).

Prove that: (i) (costheta)/(1-sintheta)=(1+sintheta)/(costheta) (ii) (1+costheta-sin^(2)theta)/(sintheta+sinthetacostheta)=cottheta (iii) 1+(tan^(2)theta)/(1+sectheta)=sectheta

The value of sectheta((1+sin theta)/(costheta)+(costheta)/(1+sintheta))-2tan^(2)theta is

Prove the following identities : (cos^(3)theta+sin^(3)theta)/(costheta+sintheta)+(cos^(3)theta-sin^(3)theta)/(costheta-sintheta)=2