If sec\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3, then the angle \(\theta\) is equal to
A
30o
B
45o
C
60o
D
90o
E
105o
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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\(\theta\) = \sqrt1
where \sqrt1 = 1
tan\(\theta\) = 1
And tan 45^\circ = 1
∴ \(\theta\) = 45^\circ
Source: Myschool Past Questions Archive (Record #32712)