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` )

Explanation

`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`

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