Problem

Problem

Let α,β,γ\alpha, \beta, \gamma be parametric angles of 3 points P,QP, Q and RR respectively lying on x2+y2=1x^2 + y^2 = 1 . If the lengths of chords AP,AQAP, AQ and ARAR are in GP where AA is (1,0)(1, 0) , then [Given α,β,γ∈(0,2π)\alpha, \beta, \gamma \in (0, 2\pi) ]. a. sin⁡α+γ4cos⁡α−γ4≥sin⁡β2\sin \frac{\alpha + \gamma}{4} \cos \frac{\alpha - \gamma}{4} \ge \sin \frac{\beta}{2} b. sin⁡(α+γ4)cos⁡(α−γ4)≤sin⁡β2\sin\left(\frac{\alpha + \gamma}{4}\right) \cos\left(\frac{\alpha - \gamma}{4}\right) \le \sin \frac{\beta}{2} c. sin⁡α2sin⁡γ2≥sin⁡β2\sin \frac{\alpha}{2} \sin \frac{\gamma}{2} \ge \sin \frac{\beta}{2} d. sin⁡α2sin⁡γ2≤sin⁡β2\sin \frac{\alpha}{2} \sin \frac{\gamma}{2} \le \sin \frac{\beta}{2}

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