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If sintheta+cosectheta=2, then sin^10the...

If `sintheta+cosectheta=2`, then `sin^10theta+cosec^10theta=?`

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`sintheta+cosecctheta=2`
`(sintheta+cosecctheta)^2=4`
`(sin^2theta+cosecc^2theta+2=4`
`sin^4thta+cosec^4theta=2`
`(sin^4theta+cosec^4theta)(sintheta+cosectheta)`
`2*2=4`
`sin^5theta+cosec^5theta+(sintheta+cosectheta)(sin^2theta+cosec^2theta-1)=4`
`sin^5theta+cosec^5theta+2(2-1)=4`
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