Question

Prove that (cosec A -sin A) (sec A-cos A)
= 1/
tan A + cott A




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Answer 1

$(coseca - sina)(seca - cosa) \\ = ( \frac{1 - {sin}^{2} a}{sina} )( \frac{1 - {cos}^{2} a}{cosa} ) \\ = \frac{ {cos}^{2}a {sin}^{2} a }{sinacosa} \\ = sinacosa \\ = \frac{sinacosa}{ {sin}^{2} a + {cos}^{2}a } \\ = \frac{1}{ \frac{ {sin}^{2} a + {cos}^{2}a }{sinacosa} } \\ = \frac{1}{ \frac{sina}{cosa} + \frac{cosa}{sina} } \\ = \frac{1}{tana + cota}$