Express sec A in term of cot A

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

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