x=sin^(-1)[(2 theta)/(1+theta^(2))],y=sec^(-1)sqrt(1+e^(2))

x=sin^(-1)((2theta)/(1+theta^(2))),y=sec^(-1)(sqrt(1+theta^(2)))

(1-sin^(2)theta)sec^(2)theta=1

The trigonometric expression: cot^(2)[(sec theta-1)/(1+sin theta)]+sec^(2)theta[(sin theta-1)/(1+sec theta)] has the value has the

tan theta= A) (sqrt(1-sin^(2)theta))/(sin theta) , B) (1)/(sec theta) , C) (sin theta)/(sqrt(1-sin^(2)theta)) D) (1)/(sqrt(1+Cot^(2)theta)

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

If (pi)/(2)

A hyperbola having the transverse axis of length 2sin theta is confocal with the ellipse 3x^(2)+4y^(2)=12 .Then its equation is x^(2)csc^(2)theta-y^(2)sec^(2)theta=1x^(2)sec^(2)theta-y^(2)cos ec^(2)theta=1x^(2)sin^(2)theta-y^(2)cos^(2)theta=1x^(2)cos^(2)theta-y^(2)sin^(2)theta=1

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

(2sin theta*tan theta(1-tan theta)+2sin theta*sec^(2)theta)/((1+tan theta)^(2))=(2sin theta)/(1+tan theta)

Prove the following trigonometric identities: cos^(2)theta+(1)/(1+cot^(2)theta)=1 (ii) (1)/(1+sin theta)+(1)/(1-sin theta)=2sec^(2)theta