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  4. The minimum value of sec2 θ + cosec2 θ is

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Q. The minimum value of $\sec^2 \, \theta + cosec^2 \, \theta$ is

Trigonometric Functions

Solution:

$\sec^{2} \theta + cosec^{2} \theta = 1 + \tan^{2} \theta + 1 +\cot^{2} \theta $
$= 2 + \left(\tan\theta - \cot\theta\right)^{2} + 2 \tan\theta \cot\theta $
$= 2 + 2 +\left(\tan\theta - \cot \theta\right)^{2} \ge4. $