If `sintheta_co s ectheta=2,` then value of `sin^(1000)theta+co s ec^(1000)theta` is equal to.

Options

A. 1
B. 2
C. 3
D. 100

Answer

b

Explanation

`sintheta+co s ectheta=2`
`sin theta+(1)/(sintheta)=2`
Now, see the value of `sintheta`
which has value 1
`sin theta=sin90^(@)=1`
`rArrsin90^(@)+(1)/(sin90^(@))=2`
`rArr1+(1)/(1)=2`
`rArr2=2`
`rArr sin^(100)theta+co s ec^(100) theta`
`rArr sin^(100)90^(@)+(1) /(sin^(100)90^(@))=(1)^(100)+(1)/((1)^(100))`