Question

If cosec 2theta=sec(theta-33 degree),where 2theta is an acute angle,find the value of theta.

Answer 1

$$\begin{gathered} \mathrm{cosec}2\mathrm{\theta }=\sec \left(\mathrm{\theta }-33\right) \\ \sec \left(90-2\mathrm{\theta }\right)=\sec \left(\mathrm{\theta }-33\right) \\ \mathrm{Comparing}, \\ 90-2\mathrm{\theta }=\mathrm{\theta }-33 \\ 3\mathrm{\theta }=123 \\ \mathrm{\theta }=41\mathrm{degree} \end{gathered}$$