Question

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.​

Answer 1

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Answer 2

Solution :-

$╰► \: 1 + {cotA} \: ^{2} = { cosec \: A }^{2}$

$\: 1 + {cot \: A}^{2} = \dfrac{1}{ {sin}^{2}A }$

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$╰►\: {sin}^{2} A = \dfrac{1}{1 + {cot}^{2}A }$

$\: sinA = \dfrac{1}{ \sqrt{1 + {cot}^{2}A } }$

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$╰► \: secA \: = \dfrac{1}{cosA}$

$sec \: A = \dfrac{1}{ \sqrt{1 - {sin}^{2}A } }$

$sec \: A = \dfrac{1}{ \sqrt{1 - \frac{1}{1 + {cos}^{2} A} } }$

$sec \: A = \dfrac{ \sqrt{1} }{ \sqrt{cot \: A} }$

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$╰► \: tan \: A \: = \dfrac{1}{cot \: A}$

Points to remember :-

$⟼ \: 1 + {cot}^{2} A = {cosec}^{2} A$

$⟼ \: sec \: A = \dfrac{1}{cosA}$

$⟼ {sin}^{2} A + {cos}^{2} A = 1$

$⟼ \: 1 + {tan}^{2} A = {sec}^{2}A$