1.

If `(sinalpha+co s ecalpha)^(2)+(cosalpha+secalpha)^(2)=k+tan^(2)alpha+cot^(2)alpha`, then the value of k isA. 1B. 7C. 3D. 5

Answer» Correct Answer - b
`(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


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