What is the simplified value of$$\ \sqrt{\frac{sec^{2} \theta+cosec^{2} \theta}{4}}$$?
Expression = $$\ \sqrt{\frac{sec^{2} \theta+cosec^{2} \theta}{4}}$$
=Â $$\ \sqrt{\frac{(\frac{1}{cos^2\ \theta})+(\frac{1}{sin^2\ \theta})}{4}}$$
=Â $$\ \sqrt{\frac{(\frac{sin^2\ \theta+cos^2\ \theta)}{sin^2\ \theta.cos^2\ \theta}}{4}}$$
= $$\sqrt{\frac{1}{4sin^2\ \theta cos^2\ \theta}}$$
= $$\sqrt{(\frac{1}{2sin\ \theta cos\ \theta})^2}$$
= $$\frac{1}{sin2\theta}=cosec2\theta$$
=> Ans - (A)
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