If `sin theta + cosec theta = 2` then the value of `sin^20 theta + cosec^20 theta`, is A. `2^10` B. `2^5` C. `2^20` D. `2`.

Explanation

`sintheta+cosectheta = 2`

`=>sintheta+1/sintheta = 2`

`=>1+sin^2theta - 2sintheta = 0`

`=>(1-sintheta)^2 = 0`

`=>sintheta = 1`

So, `cosectheta = 1/sintheta = 1`.

So, `sin^20theta +cosec^20theta = 1^20+1^20 = 1+1 = 2`