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sin^4 theta + 2 sin^2 theta ( 1 - 1/(cos...

` sin^4 theta + 2 sin^2 theta ( 1 - 1/(cosec^2 theta)) + cos^4 theta =`

Text Solution

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`sin^4theta+2sin^2theta(1-1/(cosec^2theta))+cos^4theta`
`=sin^4theta+2sin^2theta(1-sin^2theta)+cos^4theta`
`=sin^4theta+2sin^2thetacos^2theta+cos^4theta`
`=(sin^2theta+cos^2theta)^2`
`=1^2 = 1`
So, value of the required expression is `1`.
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