JAMB - Mathematics (1978 - No. 28)
If sec\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3, then the angle \(\theta\) is equal to
30o
45o
60o
90o
105o
Explicació
sec\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3
Where 1 + tan\(^2\) \(\theta\) = sec\(^2\) \(\theta\)
1 + tan\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3
2 tan\(^2\) \(\theta\) = 2
tan\(^2\) \(\theta\) = 1
tan\(\theta\) = √1
where √1 = 1
tan\(\theta\) = 1
And tan 45° = 1
∴ \(\theta\) = 45°