E-TA04 · Positivity imposes an extra parameter boundary
The numbers \(\sin x\), \(\cos^2x\), \(k-\sin x\) form an AP, where \(\displaystyle 0< x< \frac{\pi }{2}\).
Express k in terms of x and state the possible range of k.
For \(\displaystyle k= \frac{1}{2}\), find x, the three terms and their common difference.
Find the exact range of k for which all three terms are strictly positive.
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