Question
Find the least value of , where a > 0, b > 0.
Answer :
Word Count : 271
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Skip in 10
Consider the expression ( f(x) = a^2 \sec^2 x + b^2 \csc^2 x ), where ( a > 0 ) and ( b > 0 ). We can rewrite it using (\sec^2 x = 1 + \tan^2 x) and (\csc^2 x = 1 + \cot^2 x): [ f(x) = a^2 (1 + \tan^2 x) + b^2 (1 + \cot^2 x) = a^2 + a^2 \tan^2 x + b^2 + b^2 \cot^2 x = a^2 + b^2 + a^2 \tan^2 x + b^2 \cot^2 x ] Let ( t = \tan x )
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