Question

How do you give the exact value of `sec^2 300-2cos^2 150+tan 45`?

Answer 1

`sec^2(300^o) = (1 / (cos^2(300^o)))`
`cos(300^o) = cos(-60^o) = cos(60^o) = 1/2`
`cos^2(300^o) = 1/4`
`sec^2(300^o) = 4`

`cos(150^o) = - cos(30^o) = - sqrt(3)/2`
`cos^2(150^o) = 3/4`
`2 cos^2(150^o) = 3/2`

`tan(45^o) = 1`

`sec^2(300^o) - 2 cos^2(150^o) + tan(45^o)`
`= 4 - 3/2 + 1`
`= 3 1/2`