Question 41

What is the simplified value of$$\ \sqrt{\frac{sec^{2} \theta+cosec^{2} \theta}{4}}$$?

Solution

Expression = $$\ \sqrt{\frac{sec^{2} \theta+cosec^{2} \theta}{4}}$$

= $$\ \sqrt{\frac{(\frac{1}{cos^2\ \theta})+(\frac{1}{sin^2\ \theta})}{4}}$$

= $$\ \sqrt{\frac{(\frac{sin^2\ \theta+cos^2\ \theta)}{sin^2\ \theta.cos^2\ \theta}}{4}}$$

= $$\sqrt{\frac{1}{4sin^2\ \theta cos^2\ \theta}}$$

= $$\sqrt{(\frac{1}{2sin\ \theta cos\ \theta})^2}$$

= $$\frac{1}{sin2\theta}=cosec2\theta$$

=> Ans - (A)

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: