C-09-Q108mediumsingle_mcqIf cosecA−cotA=43\operatorname{cosec} A - \cot A = \dfrac{4}{3}cosecA−cotA=34, then cosecA+cotA=?\operatorname{cosec} A + \cot A = ?cosecA+cotA=?a34\dfrac{3}{4}43b43\dfrac{4}{3}34c111d−34-\dfrac{3}{4}−43ব্যাখ্যাBecause (cosecA−cotA)(cosecA+cotA)=cosec2A−cot2A=1(\operatorname{cosec} A-\cot A)(\operatorname{cosec} A+\cot A)=\operatorname{cosec}^2 A-\cot^2 A=1(cosecA−cotA)(cosecA+cotA)=cosec2A−cot2A=1, the two expressions are reciprocals. Hence cosecA+cotA=14/3=34\operatorname{cosec} A+\cot A=\dfrac{1}{4/3}=\dfrac34cosecA+cotA=4/31=43.