If `cos 25^0 + sin 25^0 = p`, then `cos 50^0` is equal to

Options

A. `sqrt(2-p^(2))`
B. `-sqrt(2-p^(2))`
C. `psqrt(2-p^(2))`
D. `-psqrt(2-p^(2))`

Answer

C

Explanation

Squaring
`1+2sin25^(@).cos25^(@)=p^(2)`
`therefore sin 50^(@)=p^(2)-1`
`therefore cos50^(@)=sqrt(1-(p^(2)-1)^(2))=psqrt(2-p^(2)) (because pgt0)`