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If sinx+cosecx=2, then find the value ...

If `sinx+cosecx=2`, then find the value of `sin^(10)x+cosec^(10)x`.

A

2

B

`2^(4)`

C

`2^(8)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`sin theta+cosec theta=2`
`impliessin^(2)theta-2sintheta+1=0`
`impliessin theta=1`
`therefore sin^(10)theta+cosec^(10)theta=1+1=2`
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