C-09-Q101mediumsingle_mcq1cosecA−1−1cosecA+1=?\dfrac{1}{\operatorname{cosec} A - 1} - \dfrac{1}{\operatorname{cosec} A + 1} = ?cosecA−11−cosecA+11=?a2tan2A2\tan^2 A2tan2Ab2cot2A2\cot^2 A2cot2Ac2sec2A2\sec^2 A2sec2Ad2cosec2A2\operatorname{cosec}^2 A2cosec2Aব্যাখ্যাCombining gives (cosecA+1)−(cosecA−1)cosec2A−1=2cot2A\dfrac{(\operatorname{cosec} A+1) - (\operatorname{cosec} A-1)}{\operatorname{cosec}^2 A - 1} = \dfrac{2}{\cot^2 A}cosec2A−1(cosecA+1)−(cosecA−1)=cot2A2. Since 1cot2A=tan2A\dfrac{1}{\cot^2 A} = \tan^2 Acot2A1=tan2A, this equals 2tan2A2\tan^2 A2tan2A.