Question

If sin $\mathrm{\theta }=\frac{\sqrt{3}}{2}$, then (cosec θ + cot θ) = ?
(a) $(2+\sqrt{3})$
(b) $2\sqrt{3}$
(c) $\sqrt{2}$
(d) $\sqrt{3}$

Answer 1

(d) $\sqrt{3}$
$$\begin{gathered} \text{Given: sin}\theta \text{=}\frac{\sqrt{3}}{2}\text{and}\cos \text{ec}\theta =\frac{2}{\sqrt{3}} \\ \cos {\text{ec}}^2\theta -{\cot }^2\theta =1 \\ \text{=>}{\cot }^2\theta =\cos {\text{ec}}^2\theta -1 \\ \text{=>}{\cot }^2\theta =\frac{4}{3}-1\left[\mathrm{Given}\right] \\ \text{=>}\cot \theta =\frac{1}{\sqrt{3}} \\ \therefore \cos \text{ec}\theta +\cot \theta =\frac{2}{\sqrt{3}}+\frac{1}{\sqrt{3}} \\ \text{=}\frac{3}{\sqrt{3}} \\ \text{=}\frac{\sqrt{3}\times \sqrt{3}}{\sqrt{3}} \\ \text{=}\sqrt{3} \end{gathered}$$