If `sin(90^(@)-theta)+theta=sqrt(2)cos(90^(@)-theta)` then the value of `co s ectheta` is

Options

A. `(1)/(sqrt(3))`
B. `(2)/(3)`
C. `sqrt((3)/(2))`
D. `(1)/(sqrt(2))`

Answer

c

Explanation

` sin(90^(@)-theta)+costheta=sqrt(2)cos(90^(@)-theta)`
`costheta+costheta=sqrt(2)sin theta`
`(2costheta)/(sintheta)=sqrt(2)`
`cottheta=(1)/sqrt(2)(rarrB)/(rarrP)`
So, `Hrarrsqrt(3)`
`therefore co s ec theta=(H)/(P)=sqrt(3)/sqrt(2)`