यदि `x="co s ec"theta-sintheta` और `y=sectheta-costheta` हो, तो x और y के बीच सम्बन्ध होगा

Options

A. `x^(2)+y^(2)+3=1`
B. `x^(2)y^(2)(x^(2)+y^(2)+3)=1`
C. `x^(2)(x^(2)+y^(2)-5)=1`
D. `y^(2)(x^(2)+y^(2)-5)=1`

Answer

b

Explanation

`x=co s ectheta-sin theta`
`y=sec theta-cos theta`
put `theta=45^(@)`
` x=sqrt(2)-(1)/sqrt(2)=(1)/sqrt(2)`
by options (b) `x^(2)y^(2)(x^(2)+y^(2)+ 3)`
`=(1)/(2)xx(1)/(2)((1)/(2)+(1)/(2)+3)=(1)/(4)(1+3)`
=1 satisfy