If \( \alpha, \beta, \gamma, \delta \) are the smallest positive angles in ascending order of ma... VIDEO
If \( \alpha, \beta, \gamma, \delta \) are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity \( k \), then the value of \( 4 \sin \left(\frac{\alpha}{2}\right)+3 \sin \left(\frac{\beta}{2}\right)+2 \sin \left(\frac{\gamma}{2}\right)+\sin \left(\frac{\delta}{2}\right) \) is equal to
(a) \( 2 \sqrt{1-k} \)
(b) \( 2 \sqrt{1+k} \)
(c) \( \frac{\sqrt{1+k}}{2} \)
(d) \( \frac{\sqrt{1-k}}{2} \)
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