Question

Express the trigonometric ratios sinA, cosecA, cotA and secA in terms of tanA.
Please answer this question fast.
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Answer 1

Sin A = Tan A cos A

Cosec A = sec A/Tan A or 1/Tan A cos A

Cot A = 1/Tan A

Sec A = Tan A/Sin A

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Answer 2

$\huge{}</p><p>\pink{given : } \\ \\ \ : sin(a) \\ \\ \ : \csc(a) \\ \\ : \cot(a) \\ \\ : \sec(a) </p><p> \\ \\ \huge{\blue{To \: \: \: find : \: }</p><p>} \\ \\ to \: \: \: express \: \: \: all \: \: \: this \: \: \: in \: \: \: term \: \: \: of \: \: \: \red{ \tan(a) } \\ \\ </p><p>\huge{\green{solution : }</p><p>}</p><p> \\ \\ \sin(a) = \frac{2 \tan( \frac{a}{2} ) }{1 + { \tan(a) }^{2} } \\ \\ \cos(a) = \frac{1 - { \tan(a) }^{2} }{1 + { \tan(a) }^{2} } \\ \\ \cot(a) = \frac{1}{ \tan(a) } \\ \\ \sec(a) = \frac{1 + { \tan(a) }^{2} }{1 - { \tan(a) }^{2} } \\ \\ </p><p>\pink{or} \\ \\ \sec(a) = \sqrt{1 - { \tan(a) }^{2} } \\ \\ \csc(a) = \frac{1 + { \tan(?a) }^{2} }{2 \tan(a) } \\ \\ </p><p>\huge{\pink{hope \: \: \: it \: \: \: helps \: \: \: you}</p><p>}</p><p></p><p>$