Write the least value of cos

Question:

Write the least value of cos2 x + sec2 x.

Solution:

We know:

cos x can take the minimum value of -1">1-1.

$\cos ^{2} x+\sec ^{2} x$

$=\frac{\cos ^{4} x+1}{\cos ^{2} x}$

$=\frac{(-1)^{4}+1}{(-1)^{2}}$

= 2

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