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JAMB Mathematics 2022 Paper

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Question : 22

Total: 39

If sec

^2

^2

θ = 3, then the angle θ is equal to?

90º
30º
45º
60º

Solution:

Concept:

Use the trigonometric identity

\sec^2\theta = 1 + \tan^2\theta

to solve for

\theta

.

Explanation:

Given:

\sec^2\theta + \tan^2\theta = 3

.

Replace

\sec^2\theta

with

1 + \tan^2\theta

.

So,

1 + \tan^2\theta + \tan^2\theta = 3

.

This simplifies to

1 + 2\tan^2\theta = 3

.

Subtract 1 from both sides:

2\tan^2\theta = 2

.

Divide both sides by 2:

\tan^2\theta = 1

.

Take the square root:

\tan\theta = \pm 1

.

In the given range,

\tan\theta = 1

when

\theta = 45^\circ

.

Therefore,

\theta = 45^\circ

.

Answer:

C.

45^\circ

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