Question Number 18523 by Tinkutara last updated on 23/Jul/17
$$\mathrm{Match}\:\mathrm{the}\:\mathrm{following} \\ $$$$\boldsymbol{\mathrm{Column}}-\boldsymbol{\mathrm{I}}\:\left(\boldsymbol{\mathrm{Trigonometric}}\:\boldsymbol{\mathrm{equation}}\right) \\ $$$$\left(\mathrm{A}\right)\:\mathrm{sin}\:\mathrm{9}\theta\:=\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{2}}\:−\:\theta\right) \\ $$$$\left(\mathrm{B}\right)\:\mathrm{sin}\:\mathrm{5}\theta\:=\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}\:+\:\mathrm{2}\theta\right) \\ $$$$\left(\mathrm{C}\right)\:\mathrm{cos}\:\mathrm{11}\theta\:=\:\mathrm{cos}\:\mathrm{3}\theta \\ $$$$\left(\mathrm{D}\right)\:\mathrm{3}\:\mathrm{tan}\:\left(\theta\:−\:\mathrm{15}°\right)\:=\:\mathrm{tan}\:\left(\theta\:+\:\mathrm{15}°\right) \\ $$$$\boldsymbol{\mathrm{Column}}-\boldsymbol{\mathrm{II}}\:\left(\boldsymbol{\mathrm{Family}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{solutions}}\right) \\ $$$$\left(\mathrm{p}\right)\:\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\frac{\pi}{\mathrm{10}},\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{q}\right)\:\frac{{n}\pi}{\mathrm{2}}\:+\:\left(−\mathrm{1}\right)^{{n}} \frac{\pi}{\mathrm{4}},\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{r}\right)\:\frac{{n}\pi}{\mathrm{7}},\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{s}\right)\:\left(\mathrm{4}{n}\:+\:\mathrm{1}\right)\frac{\pi}{\mathrm{14}},\:{n}\:\in\:{Z} \\ $$