Question

If `cottheta+tantheta=xand sectheta-costheta=y`, then
A. `xsintheta.costheta=1`
B. `sin^2theta=ycostheta`
C. `(x^2y)^(1//3)+(xy^2)^(1//3)=1`
D. `(x^2y)^(2//3)-(xy^2)^(2//3)=1`

Answer 1

Correct Answer - A::B::D
`cottheta+tantheta=x`
`or costheta/sintheta+sintheta/costheta=x`
`or 1=xsinthetacostheta`
Now, `sectheta-costheta=y`
`1/costheta-costheta=y`
`or sin^2tehta=ycostheta`
`Now, x^2y=1/(sin^2thetacos^2theta).sin^2theta/costheta=1/cos^3theta`
`and xy^2=sin^3theta/cos^3theta`
`:. (x^2y)^(2//3)=1/cos^2theta-sin^2theta/cos^2theta=1`