1.

The set of values of `lambda in R`such that `sin^2theta+costheta=lambdacos^2theta`holds for some `theta,`is`(-oo,1]`(b) (`-oo,-1]``varphi`(d) `[-1,oo`)

Answer» `sin^2theta+costheta=lambdacos^2theta`
`sin^2theta/cos^2theta+cos^2theta/cos^2theta=lambdacos^2theta/cos^2theta`
`tan^2theta+sectheta=lambda`
`sec^2theta-1+sectheta-lambda=0`
`sec^2theta+sectheta-(lambda+1)=0`
`sectheta=(-1pmsqrt(1+4(lambda+1)))/2`
`=(-1pmsqrt(4lambda+5))/2`
`4lambda+5>=0`
`lambda>=-5/4`
`(-1pmsqrt(4lambda+5))/2>=1`
`sqrt(4lambda+5)>=3`
`4lambda+5>=9`
`4lambda>=4`
`lambda>=1-(1)`
`lambda<=-1-(2)`
`lambda in[-1,oo)`
Option D is correct.


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