Trigonometry Practice Test 2

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Question : 7 of 22

Marks: +1, -0

If

x=\cos^2θ+\sec^2θ,

which one of the following is correct?

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

Solution:

x=\cos^2θ+\sec^2θ

We know that

(a-1/a)^2≥0

⇒a^2+1/a^2-2 ≥ 0

Put

a=\cos θ

∴\cos^2θ+1/{\cos^2θ} ≥ 2

⇒\cos^2θ+\sec^2θ ≥ 2

⇒x ≥ 2

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