Word Count : 420

---

We are asked to find the least value of the expression: \[ a^2 \sec^2 x + b^2 \csc^2 x \] where \( a > 0 \) and \( b > 0 \). ### Step 1: Understand the function - \( \sec^2 x = \frac{1}{\cos^2 x} \) - \( \csc^2 x = \frac{1}{\sin^2 x} \) Thus, the given expression becomes: \[ f(x) = a^2 \cdot \frac{1}{\cos^2 x} + b^2 \cdot \frac{1}{\sin^2 x} \] ### Step 2: Analyze the behavior of the expression We want to minimize the function \( f(x) = a^2 \sec^2 x + b^2 \csc^2 x \), where \( \sec^2 x \) and \( _________ ______ _____ _________ ______ ________ ________ ____ ___ _____ _________ ___.
___ ______ _________ _____ ______ ____ ______ ___ _____ ____ _________ _______.
_______ _____ _______ ________ __________ _________ ____ _________.
________ _______ ___ _____ ___ _____ _____.
__________ _____ ________ _______ __________.
___ _____ _______ ______ ________ _______ ______.
________ _____ __________ ___ _____ ________ ______ _____.
__________ ___ _________ _________ _______ _________ _____ ____ _______ _______ _____.
_____ ___ ___ ____ ___.
________ _________ ___ ________ _________ ________ ____ ______ ____ ____ ___.
_____ _____ ___ ________ ___ ________.
____ __________ _________ ___ _____ ____ ____ _________ _________ _________ ____ ______.
_____ _____ __________ _____ ______ ____ ____ ____ _________ __________.
________ ________ _______ _________ ______ ______ _____ ____ _______ ____ _______ ________.
___ ___ ____ _________ _______ _________ ________ _________ _______ __________ ______.
_____ ____ _____ _______ ____ ____ ___.
__________ _____ ________ _____ __________ _______ ____ _________ ______ ______ _____ ________.
___ _______ __________ ______ _______ ________ _________ ________ ________ _____ ___.
______ _______ _________ _______ ________ ________ ________ __________ ____ _______ __________.
_________ _____ ___ _______ _______ ____ __________ ________ ______ ____ __________.
_______ ___ _____ _________ ______ _____.
_____ ________ ___ ___ ____ _________.
_________ __________ ___ _____ ____ ___ _______ ________ __________ ___ _______ ______.
__________ ____ ____ ____ ______ ______ ___ ____ _______ ___.
______ ____ __________ ____ ________.
____ _____ _______ ___ __________ ______ ___ ____ ____ ________.
___ __________ __________ _______ _________ _________ _______.
_________ ________ ____ _______ ____ ___ ____ _________ ___ ______ ______.
____ __________ _______ ___ ___ __________ ____ ________ _____ ________.
_____ __________ _________ _________ ____ _______.
_________ _______ ____ _______ ____ _________ ______ ____ ___.
_________ _____ ___ __________ ___ ___ _______ ____ ____ ____ ________.
________ ____ __________ ___ _______ __________ ___ _______.
_______ ______ _____ _______ _____ _____ ______ ______ _____.
__________ ________ ___ _________ _______ ______.
Get Full Answer on WhatsApp