If `sin^6theta+cos^6theta+kcos^2(2theta)=1`, then `k` is

Explanation

`sin^6theta=cos^6theta=(sin^2theta+cos^2theta)(sin^4theta+costheta-sin^2thetacostheta)=1`

`(sin^2theta+cos^2theta)^2-3sin^2thetacos^2theta)=1`

`=1-3sin^2thetacos^2theta`

`=1-3/4*sin^2(2theta)`

`=1/4+3/4cos^2 2theta`

`3cos^2 2theta+4kcos^2 2 theta=3`

`cos^2 2 theta(3+4k)=3`

`k=3/4+tan^2theta`

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