If sec\(^2\)θ + tan\(^2\)θ = 3, then the angle θ is equal to?
A
90º
B
30º
C
45º
D
60º
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Given that sec\(^2\)\theta + tan\(^2\)\theta = 3
Where sec\(^2\)\theta = 1 + tan\(^2\)\theta
: 1 + tan\(^2\)\theta + tan\(^2\)\theta = 3
2tan\(^2\)\theta = 3 - 1
2tan\(^2\)\theta = 2
divide both sides by 2
tan\(^2\)\theta = 1
tan\theta = \sqrt1
tan\theta = 1
\theta = tan\(^{-1}\) (1)
\theta = 45º
Source: WAEC / JAMB / NECO Classroom Archive (Record #64282)