Question

prove that sec theta upon tan theta + cot theta is equal to sin theta​

Answer 1

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Answer 2

Step by step explanation:


$\frac{ \sec(a) }{ \tan(a) + \cot(a) } = \sin(a)$
$lhs = \frac{1}{ \cos(a) } \times \ \tan(a)+\cot(a)$
$= \frac{1}{ \cos(a) } \times \frac{ \sin(a) }{ \cos(a) } + \frac{ \cos(a) }{ \sin(a) }$
$= \frac{1}{ \cos(a)} \times \frac{ \sin(a) \times \sin(a) }{ \cos(a) \times \sin(a) } + \frac{ \cos(a) \times \cos(a) }{ \sin(a) \times \cos(a) }$
$= \frac{1}{ \cos(a) } \times \frac{ { \sin }^{2} (a)}{ \cos(a) \times\sin(a) } + \frac{ { \cos}^{2}(a) }{ \sin(a )\times \cos(a) }$
–――――――― {making denominator equal}
$= \frac{1}{ \cos(a) } \times \frac{ { \sin }^{2} (a) + \cos ^{2}(a) }{ \sin(a) \times \cos(a) }$