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If 2sec^2 alpha- sec^4 alpha-2 cosec^2 a...

If `2sec^2 alpha- sec^4 alpha-2 cosec^2 alpha+cosec^4 alpha=15/4` then `tan alpha=`

A

`1//sqrt2`

B

`1//2`

C

`1//22sqrt2`

D

`-1//sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`2sec^2alpha-sec^4alpha-2cosec^2alpha+cosec^4alpha=15/4`
`or 2(sec^2alpha-cosec^2alpha)+(cosec^2alpha+sec^2alpha)xx(cosec^2alpha-sec^2alpha-sec^2alpha)=15/4`
`or (cosec^2alpha-sec^2alpha)[cosec^2alpha+sec^2alpha-2]=15/4`
`or 4(cot^2alpha-tan^2alpha)[cosec^2alpha+sec^2alpha)=15`
`or4(cot^4alpha-tan^4alpha)=15`
`or 4(1-tan^8alpha)=15tan^4alpha`
`or 4tan^8alpha+15tan^4alpha`
`or 4tan^8alpha+154tan^4alpha-4=0`
`or (4tan^4alpha-1)(tan^4alpha+4)=0`
`or tan^4alpha=1/4ot tan^4alpha=-4`
`or tan^2alpha=pm1/2`
`or tan^2alpha=+1/2`
`or tanalpha=pm1/sqrt2`
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