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Home » In math olympiad context, fractional students possible in intermediate steps? No. - Midis

In math olympiad context, fractional students possible in intermediate steps? No. - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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Let \( f(x) = (\sec x + \csc x)^2 = \left( \frac{1}{\cos x} + \frac{1}...
f(x) = \left( \frac{\sin x + \cos x}{\sin x \cos x} \right)^2
Let \( s = \sin x + \cos x \), \( p = \sin x \cos x \). Note:
s^2 = \sin^2 x + \cos^2 x + 2\sin x \cos x = 1 + 2p \Rightarrow p = \f...
f(x) = \left( \frac{s}{p} \right)^2 = \left( \frac{s}{(s^2 - 1)/2} \ri...
Now, for \( x \in (0, \frac{\pi}{2}) \), \( s = \sin x + \cos x = \sqr...
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