If `(sinalpha+co s ecalpha)^(2)+(cosalpha+secalpha)^(2)=k+tan^(2)alpha+cot^(2)alpha`, then the value of k is

Options

A. 1
B. 7
C. 3
D. 5

Answer

b

Explanation

`(sinalpha+co s ecalpha)^(2)+(cosalpha+secalpha)^(2)=k+tan^(2)alpha+cot^(2)alpha`
Put `alpha=45^(@)`
`rArr (sin45^(@)+co s ec45^(@))^(2)=k+1+1`
`(1)/(2)+2+(2sqrt(2)xx(1)/(2))+(1)/(2)+2+(2sqrt(2)xx(1)/sqrt(2))`
`rArr4(1)/(2)+4(1)/(2)=k+2`
k=7