Question

If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then

Options

• f(x) < 1

• f(x) = 1

• 1 < f(x) < 2

• f(x) ≥ 2

Answer 1

\[f\left( x \right) = \cos^2 x + \sec^2 x\]
\[ = \cos^2 x + \sec^2 x - 2\cos x\sec x + 2\cos x\sec x\]
\[ = \left( \sec x - \cos x \right)^2 + 2\]
\[ \therefore f\left( x \right) \geq 2 \forall x \left[ \left( \sec x - \cos x \right)^2 \geq 0 \forall x \right]\]

Hence, the correct option is answer f(x) ≥ 2.