If sec\(^2\)θ + tan\(^2\)θ = 3, then the angle θ is equal to?
MATHEMATICS
JAMB 2022
If sec\(^2\)θ + tan\(^2\)θ = 3, then the angle θ is equal to?
- A. 90
- B. 30
- C. 45
- D. 60
Correct Answer: C. 45
Explanation
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
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