Express the trigonometry ratioes sin a,tan a,in terms of cot a

1.	Express the trigonometry ratioes sin a,tan a,in terms of cot a
Answer» We have to express the trigonometric ratios sin A, sec A\xa0and tan A\xa0in terms of cot A.For sin A,By using identity {tex}cosec ^ { 2 } A - \\cot ^ { 2 } A = 1{/tex}{tex}\\Rightarrow cosec ^ { 2 } A = 1 + \\cot ^ { 2 } A{/tex}{tex}\\Rightarrow \\frac { 1 } { \\sin ^ { 2 } A } = 1 + \\cot ^ { 2 } A{/tex}{tex}\\Rightarrow \\sin ^ { 2 } A = \\frac { 1 } { 1 + \\cot ^ { 2 } A }{/tex}{tex} \\Rightarrow \\quad \\sin A = \\frac { 1 } { \\sqrt { 1 + \\cot ^ { 2 } A } }{/tex}For tan A,{tex} \\tan A = \\frac { 1 } { \\cot A }{/tex}

Discussion