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Home » Next, find $\|\mathbfq\|^2$: - AssociationVoting

Next, find $\|\mathbfq\|^2$: - AssociationVoting

📅 May 16, 2026 👤 scraface

May 16, 2026

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Solution: We are to maximize the expression
for $0 < x < \frac{\pi}{2}$.
First, expand both squares:
Now sum them:
\sec^2 x + \csc^2 x + 2\sec x \csc x + 1 + 2\sin x \cos x
Recall that $\sec^2 x = 1 + \tan^2 x$, $\csc^2 x = 1 + \cot^2 x$, but...
\sec^2 x + \csc^2 x = \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x} = \frac{...
Also, $\sec x \csc x = \frac{1}{\sin x \cos x}$, so:
2\sec x \csc x = \frac{2}{\sin x \cos x}
And $2\sin x \cos x$ remains.

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