Question

prove that (1+ cotA-cosecA) (1+ tanA + secA)=2​

Answer 1

Answer:

Easy way is convert them in sin and cos

$(1 + \frac{ \cos(x) }{ \sin(x) } - \frac{1}{ \sin(x) } )(1 + \frac{ \sin(x) }{ \cos(x) }{+ \frac{1}{ \cos(x) } } ) \\\\ = \frac{1 + \cos(x) - \sin(x) }{ \sin(x) } \times \frac{1 + \sin(x) - \cos(x) }{ \cos(x) } \\ \\ = \frac{1 - ( \cos(x) - \sin(x) ) {}^{2} }{ \sin(x) \cos(x) } \\ \\ = \frac{1 - ( \cos {}^{2} (x) + \sin {}^{2} (x) - 2 \sin(x) \cos(x) }{ \sin(x) \cos(x) } \\ \\ = \frac{1 - 1 + 2 \sin(x) \cos(x) }{ \sin(x) \cos(x) }\\ \\ = 2$