JAMB - Mathematics (2022 - No. 22)
If sec\(^2\)θ + tan\(^2\)θ = 3, then the angle θ is equal to?
90º
30º
45º
60º
Penjelasan
Given that sec\(^2\)θ + tan\(^2\)θ = 3
Where sec\(^2\)θ = 1 + tan\(^2\)θ
: 1 + tan\(^2\)θ + tan\(^2\)θ = 3
2tan\(^2\)θ = 3 - 1
2tan\(^2\)θ = 2
divide both sides by 2
tan\(^2\)θ = 1
tanθ = √1
tanθ = 1
θ = tan\(^{-1}\) (1)
θ = 45º