Test Index

Trigonometry Practice Test 2

© examsnet.com

Question : 7 of 22

Marks: +1, -0

If

x=\cos^2\theta+\sec^2\theta,

which one of the following is correct?

0 < x < 1
1 < x < 2
x = 2
x ≥ 2
None of these

Solution:

Concept:

Use the inequality

a+\dfrac{1}{a}\ge 2

for

a>0

.

Explanation:

Let

a=\cos^2\theta

.

Then

\sec^2\theta=\dfrac{1}{\cos^2\theta}=\dfrac{1}{a}

.

So,

x=a+\dfrac{1}{a}

.

Since

a>0

, we have

a+\dfrac{1}{a}\ge 2

.

Thus,

x=\cos^2\theta+\sec^2\theta\ge 2

.

Equality occurs when

\cos^2\theta=1

, giving

x=2

.

Therefore, the minimum value of

x

is

2

, so

x\ge 2

.

Answer:

x\ge 2

, which matches option D.

© examsnet.com

Go to Question:

Prev Question

Next Question