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The value of 3(sin^4t+cos^4t-1)/(sin^6t+...

The value of `3(sin^4t+cos^4t-1)/(sin^6t+cos^6t-1)` is equal to __________

Text Solution

Verified by Experts

The correct Answer is:
2
`sin^4t+cos^4t-1=(sin^2t=cos^2t)^2-2sin^2tcos^2t-1`
`=-2sin^2tcos^2t`
`sin^6t+cos^6t-1=(sin^2t+cos^2t)^3-3sin^2tcos^2t-1`
`=-3sin^2tcos^2t`
Hence, `3(sin^4t+cos^4t-1)/(sin^6t+cos^6t-1)`=2`
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