Question

tan theta + 1/tan theta =Sec theta Cosec theta
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Answer 1

$lhs = \tan( \theta) + \frac{1}{ \tan( \theta) } \\ = \frac{sin \theta}{ \cos( \theta) } + \frac{\cos( \theta) }{\sin( \theta) } \\ = \frac{ \sin^{2} ( { \theta }) + \cos ^{2} ( \theta) }{sin\theta \times \cos(\theta) } \\ = \frac{1}{ \sin(\theta) \cos(\theta) } \\ = \sec(\theta) \csc(\theta) = rhs$