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If 15 sin^(4)alpha+10cos^(4)alpha=6, the...

If `15 sin^(4)alpha+10cos^(4)alpha=6`, then the value of `8 cosec^(6)alpha+27 sec^(6)alpha` is

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Verified by Experts

The correct Answer is:
65
Divide by `cos^4alpha`
`rArr 15tan^4alpha+10=6sec^4alpha`
`rArr 15tan^4alpha+1=6(1+tan^2alpha)^2`
`rArr (3tan^2alpha-2)^2=0`
`:. Tan^2alpha=2//3`
`:. 8cosec^2alpha+27sec^2alpha=sec^2alpha(8cot^2alpha+27)`
`=5/3(8xx3/2+27)=65`
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